For the second time in three days, prosecutors announced corruption charges Thursday against a New York state lawmaker, this time accusing a legislator of accepting bribes from businessmen who wanted his help in running and maintaining adult day-care centers. A 36-page complaint charged Sen. Eric Stevenson, who represents the 79th District in the Bronx, with accepting about $22,000—most of it stuffed into envelopes and handed over at a number of secretly recorded meetings—between April 2012 and this month. Stevenson, 46, who was elected in 2010, was charged with fraud, conspiracy and bribery and could face at least 20 years in...