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.
I think I understand but my rendering program does not generate UV maps and I need a program that generates UV maps, Michael has listed some programs that can generate them but the demos do not allow the export of the map (you cannot save) so I couldn't test the program and the resulting map .... so I couldn't create anything.
Now I simply used a dirt map to simulate the dirty bodywork but it is not the same as a 3d painter in my opinion .... the effect is much more unreal than a dedicated map
about easy easy Paint or texture on 3D volumes take a look to the Paint 3D given (so free) by Windows (if you have this OS)
Not headaches and not long learning curves! :)
You can insert any volumes made by Moi ;) OBJ, STL, FBX...