The actual amounts that you will need will vary based on the types of cocoa and corn syrup used, and also how glossy or richly colored you want your paint. Use your personal preference to guide you.
Mix approximately 2-3 Tablespoons of cocoa powder into 1 cup of corn syrup and stir well. If your mixture has a hard time combining, you can microwave it for 20 seconds and let cool, then stir well.
The more corn syrup you add, the thinner and more spreadable your paint will be. The more chocolate you add, the thicker and more pigmented.