Hi Tony,

In 3D coat, you will paint over the UV map, this map can then be exported with your 3D model, and rendered in any 3D renderer.
If you want to paint, one of the best tool for this is Substance Painter : https://www.substance3d.com/products/substance-painter/

You need 1st to generate your UV map, in a 3D software, then you export this map to Substance painter with your 3D model, and do your paint there.