Jim,
I am a historian, not a demographer, but I have found most scholars accept rates of natural increase between 24% and 30% in each decade for the 19th century US slave population. Fogel and Engerman, Time on the Cross: Evidence and Methods, a Supplement, discuss demographics at length, and find a natural population growth among US slaves of 2.3% growth per year (page 31). The increase of slaves from 1.19 million people in 1810 to 3.95 million people in 1860 is easily attributable to this natural cause.

The 1810 and 1820 censuses, as K Wyer Lane pointed out, did not include some Spanish possessions, such as the territories that would later become Florida and Texas.

Comments on Theodore Weld's arguments, cited in an earlier response:

Recent scholarship embraces Weld's conclusions that the internal slave trade was fundamental to the vitality of antebellum Southern slavery (see Robert H Gudmestad, A Troublesome Commerce: The Transformation of the Interstate Slave Trade (2003), and Steven Deyle, Carry Me Back: The Domestic Slave Trade in American Life (2005)), but this trade redistributed the population within the slave territories; it did not increase the total population.

Weld's assertions that slaveowners bred slaves for the market like animal likestock was polemical, not factual. There is no credible evidence yet found of such slave-breeding.

The 1808 ban on the African slave trade was essentially effective (except, of course, in the unfortunate experience of the few thousands of people who were pirated from Africa to the US in violation of the law). The number of slaves thus imported was not a significant factor in population growth. You can examine this in the 1870 census by analyzing the numbers of persons whose birthplace was in Africa.

I recommend you seek articles specifically about demographics,
such as J. E. Eblen, "Growth of the black population in antebellum America, 1820-1860," Population Sudies (Cambridge), vol 26 no. 2 (July 1972), pp. 273-89.