I recently dyed a pair of leather shoes.
What I did was go to a good small independent shoe repair shop and asked if he would dye my shoes black. He said that it would cost me $35.00 for him to dye my brown shoes black and he said it was easy to do, just buy the dye and do it myself. I bought the appropriate bottle of dye from the shoe repair shop guy and dyed my own shoes for under $8.00/Canadian. It was simple and I dyed them the right way. They look great.
I am an artist and my experience is that THE SURFACE HAS TO BE CLEANED WELL FIRST, then apply a base coat (can be bought in clear, white or black, or you can add your own tint to one of these), has to be applied to the surface first, then the acrylic paint applied. The base coat helps the acrylic paint adhere to the surface., and less likely to peel. It would be helpful to put a sealant on the final finished acrylic paintwork.
I plan to do some artwork on some leather shoes, and also paint on, as I've described here, on another pair of Nubuck platform shoes. All the materials can be bought at a good artist supply store. The employees in these stores often have good advice and suggestions too.
Good luck with your project. I hope I've been of some help to answer your question. Ciao! :)