Many words lose their relevance and thus usage over time. Fortunately, slavemongering, is among them.
A monger is defined as a dealer or trader. To monger is to promote or deal in something specified. It is generally used in a composition. Thus a costermonger is an itinerant fruit-seller, a fellmonger is a dealer in skins, a fishmonger peddles fish, and an ironmonger is a dealer in iron goods.
Walter William Skeat’s An Etymological Dictionary of the English Language, suggests as possible source of the word.
monger, mangere a dealer merchant formed with suffix ere from mang ian – to traffic barter gain by trading.
The relationship to the Lat[in] mango, a dealer in slaves, is not clear but the [English] word does not appear to have been borrowed from it. 
Slaves were “inseparable from any species of private property” and since “titles to slaves were transferable,” their owners had the power of conveyance.  Thus the legality of slavemongering, or the trafficking of slaves, was firmly established in the Antebellum South.
Slave owners seemed somewhat ambivalent to the idea of slavemongering. Some despised the idea but took advantage of it non-the-less. Thus one who found the sale of a bondsman distasteful or even bordering on amoral, could unburden themselves of their human property using a professional.
Franklin & Armfield had the distinction of being the the largest slave-trading enterprise in the South at least during the period prior to the Panic of 1837. Formed in 1828, its principles were John Armfield and Isaac Franklin. They each “accumulated fortunes in excess of a half million dollars” before retiring. 
Hundreds of small entrepreneurs engaged in slave trade but only a few made large sums of money. Among these few was Nathan Bedford Forrest who “was the largest slave trader in Memphis during the late 1850’s; he was reputed to have made a profit of $96,000 in a single year.” 
 Walter William Skeat, An Etymological Dictionary of the English Language, accessed on the internet via Google Books, November 22, 2008 here.
 Kenneth M. Stampp, The Peculiar Institution: Slavery in the Ante-Bellum South.