There would also be all kinds of problems with bills of sale and other methods of proving title. Under the law any owner, not just the slave importer, had to prove the slave in question had been brought into the country at least five years before the prosecution. Sounds like for many planters it would have been way too much trouble and risk.
Here's a very VERY rough estimate using my World Almanac.
The almanac doesn't have 1810 data, but it does have 1820, 1860, and 1900.
Black population in 1820: 1.77 million. 1860: 4.44 million. 1900: 8.83 million.
The 1860 number was 2.5 times the 1820 number. 1900 was 2.0 times 1860.
Since there was no importation of slaves and probably very little immigration of blacks from 1860 to 1900, we take 2.0 as the natural increase. Applying this to the 1820 population, we'd expect 3.54 million blacks in 1860.
But there were actually 4.44 million. So we estimate that 900,000 were brought in.
Yep, it's VERY rough. But it illustrates the kind of thing that could be calculated, if you could get a good estimate of the expected natural birth/death rates in the pre-1860 period.