Raleigh, NC, has an average overnight low of 70 degF in July and August. I'll assume a corresponding relative humidity of 95%. You want inside air to be 82 degF and 50% relative humidity. The sensible load in your favor from the 12 degF temperature difference would be about 1300 BTU/h per 100 cfm of air. The latent difference required to remove 25 grains/lb of excess humidity from 100 cfm of air would be about 1600 BTU/hr. Add to that the 400 W (~1300 BTU/hr) from a typical small dehumidifier, since the dehumidifier turns that electricity into heat; the extra heat from temperatures higher than the overnight low (most of the time); and the heat gain from sun, walls, windows, appliances, and people. In the middle of summer, you would probably end up with an inside temperature well over 100 degF.
If you're the DIY type, you can get a modestly efficient ductless mini-split online for about $1500 and install it yourself. If you do that, let us know how it goes.