This depends a lot on what you are painting onto the vinyl and how the vinyl is being used.
If you are working with vinyl fabric and want a complete color change: you are probably out of luck, but you can experiment with dyes for synthetic fabrics. I know these will dye clear vinyl and some pleathers, so it might be worth a shot.
If you are painting designs that need to be painted or are changing the color of shoes: Angelus leather paint is the go-to brand for this.
If you are painting shoes that don’t flex too much (so more shoes than boots): You might have luck with Design Master Colortool spray. This is a spray paint meant for both real and faux florals, so it is soft, and can be used on fabrics. Some cosplayers have had luck using this on shoes, though I don’t know if I would test my luck on something that bends a lot/is floppy like boots.
If you need large, geometric designs or anything else with hard edges and a single color: heat transfer vinyl will be your friend! Be sure to be VERY careful with the heat and use a press cloth. You don’t need a fancy die-cutting machine to use it, either, if you just need a one-off design and have good control with scissors and/or a craft knife. If doing multiples of a design or a very delicate design, you may need a machine (or to borrow a friend’s).
Good luck! I hope that helps :]
—Fabrickind / Q&A Staff / Twitter