Ultimately, the business of slavery was successful because it made some degree of economic sense.
The reasons that this business was successful start with the fact that sugar and later cotton were in great demand in Europe. Because they were in such great demand, planting them would be profitable provided costs were not too high. Slavery entered the picture because it was very unlikely that free people would be attracted to do the work needed to grow sugar in the Caribbean or cotton in the American South. It was very hard work in tough conditions and there were many easier jobs for free people. Therefore, slaves were needed. This demand for slaves meant that the slave trade was a lucrative business as well.
So, slavery was a successful business because it allowed both slave traders and planters to make money.
The Diligent, a French ship, made one slave-trading voyage in 1731. It did not make a profit, and thereafter traded in other commodities.