Have to agree dye is what you need. Lacquer based paints will probably eat into the leather and destroy it, and enamel will probably not bond to the material.
what you need is vinyl paint. I use SEM, but it's up to about $12 a can and you have to go to a auto paint supply store. Try one of the generic brands they carry in the parts store. The SEM lasts for years. I've done seats and all in the past. Good stuff, renews appearance with little effort and looks like the part came that way.