R.J.
Ditto the RIT dye.
I'd recommend going to a fabric store... since there are about 50 colors of RIT dye (including dark wash denim), but the grocery & drug stores usually only have 5 or 6 colors. There are also other fabric dyes... but RIT is the most commonly used.
You measure RIT by lbs of fabric to be dyed, so for slip covers, you'll probably be buying several packages. And don't forget the salt!!!
You will have to rinse it at LEAST 5 or 6 times in order to get all of the excess dye out of it (or it will transfer onto other things, like the pants of people sitting on the couch. particularly when damp... so hot sweaty days = bad news if you haven't rinsed the heck out of it).
Also, you can use a color remover before hand... or just dye over the existing color.
For washing machine cleanup (you can also use a large garbage can and a hose, but it's more labor intense)... do 1 or 2 empty loads afterward. Using colorsafe bleach in the empty load will also help.