1. The only substantive record from the Constitutional Convention of somebody speaking on the clause - its proposal by Pickney - says that Congress should have the suspension power.
2. The testimony of a delegate in attendence at the Constitutional Convention, Robert Yates, says that the Constitution gives Congress the suspension power.
3. The testimony from the state ratification conventions indicates that they understood Congress to have the suspension power.
4. The testimony of two very prominent founding fathers, Thomas Jefferson and Richard Henry Lee, says that Congress has the suspension power.
5. The testimony of the most prominent and venerated Chief Justice in US History, John Marshall, says that Congress has the suspension power.
6. The testimony of St. George Tucker, "America's Blackstone" and the first major legal scholar to analyze the Constitution, says Congress has the suspension power. So does that of another prominent legal scholar William Rawle.
7. The testimony of at least four other pre-war Supreme Court Justices - that of Taney, Story, Saulsbury, and Curtis - says that Congress has the suspension power.
By contrast only Lincoln says they do not, and only you, Rehnquist, and O'Conner writing 140 years after the fact seem to agree with Lincoln's tortured defense for suspending the writ. Your case, to put it mildly, is in severe want of evidence, to say nothing of legal scholarship and good old common sense.
READ IT AND WEEP:
"The privileges and benefit of the writ of Habeas Corpus shall be enjoyed in this Government, in the most expeditious and ample manner; and shall not be suspended by the Legislature, except upon the most urgent and pressing occasions, and for a limited time not exceeding months." - Charles Pickney, announcing the proposal to limit the suspension of habeas corpus, Constitutional Convention, 1787
"The people by adopting the federal constitution, give congress general powers to institute a distinct and new judiciary, new courts, and to regulate all proceedings in them, under the eight limitations mentioned in a former letter; and the further one, that the benefits of the habeas corpus act shall be enjoyed by individuals." - Richard Henry Lee, Anti-Federalist #16, "Federal Farmer"
"In the same section it is provided, that "the privilege of the writ of habeas corpus shall not be suspended, unless when in cases of rebellion and invasion, the public safety may require it." This clause limits the power of the legislature to deprive a citizen of the right of habeas corpus, to particular cases viz. those of rebellion and invasion; the reason is plain, because in no other cases can this power be exercised for the general good." - Robert Yates, delegate to the Constitutional Convention, Anti-Federalist #9, "Brutus"
"The safest and best restriction, therefore, arises from the nature of the cases in which Congress are authorized to exercise that power [of suspending habeas corpus] at all, namely, in those of rebellion or invasion. These are clear and certain terms, facts of public notoriety, and whenever these shall cease to exist, the suspension of the writ must necessarily cease also." - Judge Francis Dana, presenting the Constitution to the Massachusetts Ratification Convention
"In the United States, it can be suspended, only, by the authority of congress; but not whenever congress may think proper; for it cannot be suspended, unless in cases of actual rebellion, or invasion. A suspension under any other circumstances, whatever might be the pretext, would be unconstitutional, and consequently must be disregarded by those whose duty it is to grant the writ." - St. George Tucker, Commentaries, 1803
"The decision that the individual shall be imprisoned must always precede the application for a writ of habeas corpus, and this writ must always be for the purpose of revising that decision, and therefore appellate in its nature. But this point also is decided in Hamilton's case and in Burford's case. If at any time the public safety should require the suspension of the powers vested by this act in the courts of the United States, it is for the legislature to say so. That question depends on political considerations, on which the legislature is to decide." - Justice John Marshall, writing for the majority in Ex Parte Bollman and Swartwout, United States Supreme Court, 1807
"Those respecting the press, religion, & juries, with several others, of great value, were accordingly made; but the Habeas corpus was left to the discretion of Congress, and the amendment against the reeligibility of the President was not proposed by that body." - Thomas Jefferson, Autobiography, 1821
"The Constitution seems to have secured this benefit [habeas corpus] to the citizen by the description of the writ, and in an unqualified manner admitting its efficacy, while it declares that it shall not he suspended unless when, in case of rebellion or invasion, the public safety shall require it. This writ is believed to be known only in countries governed by the common law, as it is established in England; but in that country the benefit of it may at any time be withheld by the authority of parliament, whereas we see that in this country it cannot be suspended even in cases of rebellion or invasion, unless the public safety shall require it. Of this necessity the Constitution probably intends, that the legislature of the United States shall be the judges. Charged as they are with the preservation of the United States from both those evils, and superseding the powers of the several states in the prosecution of the measures they may find it expedient to adopt, it seems not unreasonable that this control over the writ of habeas corpus, which ought only to be exercised on extraordinary occasions, should rest with them. It is at any rate certain, that congress, which has authorized the courts and judges of the United States to issue writs of habeas corpus in cases within their jurisdiction, can alone suspend their power" - William Rawle, "A View of the Constitution of the United States of America," 1826
"It would seem, as the power is given to congress to suspend the writ of habeas corpus in cases of rebellion or invasion, that the right to judge, whether exigency had arisen, must exclusively belong to that body." - Justice Joseph Story, "Commentaries on the Constitution of the United States," Book 3, Chapter XXXII, § 1336, 1833
"And who could hold for a moment, when the writ of habeas corpus cannot be suspended by the legislature itself, either in the general government or most of the States, without an express constitutional permission, that all other writs and laws could be suspended, and martial law substituted for them over the whole State or country, without any express constitutional license to that effect, in any emergency? Much more is this last improbable when even the mitigated measure, the suspension of the writ of habeas corpus, has never yet been found proper by Congress, and, it is believed, by neither of the States, since the Federal Constitution was adopted." - Justice Levi Woodbury, dissent in Luther v. Borden, United States Supreme Court, 1849
"With such provisions in the constitution, expressed in language too clear to be misunderstood by any one, I can see no ground whatever for supposing that the president, in any emergency, or in any state of things, can authorize the suspension of the privileges of the writ of habeas corpus, or the arrest of a citizen, except in aid of the judicial power. He certainly does not faithfully execute the laws, if he takes upon himself legislative power, by suspending the writ of habeas corpus, and the judicial power also, by arresting and imprisoning a person without due process of law." - Justice Roger B. Taney, Ex Parte Merryman, US Circuit Court of Appeals, 1861
"There has been much discussion concerning the question whether the power to suspend the "privilege of the writ of habeas corpus" is conferred by the Constitution on Congress, or on the President. The only judicial decisions which have been made upon this question have been adverse to the power of the President.Still, very able lawyers have endeavored to maintain -- perhaps to the satisfaction of others -- have maintained, that the power to deprive a particular person of the "privilege of the writ," is an executive power. For while it has been generally, and, so far as I know, universally admitted, that Congress alone can suspend a law, or render it inoperative, and consequently that Congress alone can prohibit the courts from issuing the writ, yet that the executive might, in particular cases, suspend or deny the privilege which the writ was designed to secure. I am not aware that any one has attempted to show that under this grant of power to suspend "the privilege of the writ of habeas corpus," the President may annul the laws of States, create new offences unknown to the laws of the United States, erect military commissions to try and punish them, and then, by a sweeping decree, suspend the writ of habeas corpus as to all persons who shall be "arrested by any military authority." I think he would make a more bold than wise experiment on the credulity of the people, who should attempt to convince them that this power is found in the habeas corpus clause of the Constitution. No such attempt has been, and I think none such will be made. And therefore I repeat, that no other source of this power has ever been suggested save that described by the President himself, as belonging to him as commander-in-chief." - Justice Benjamin R. Curtis, "Executive Power," 1862
Learned opinions all. But the Constitution is silent on who has the sole authority to suspend habeas corpus. In matters where actions or laws seem to conflict with the Constitution then it is up to the Supreme Court to decide whether those actions or laws have, in fact, violated the Constitution. Until the court does make such a decision then Lincoln's were not unconstitution just because you say they were.