Okay, what it is you need is the texture template. I’m assuming you do not know what that is, so I will explain it.
The model is made up of polygons. Those polygons are flattened out to a 2D map for reference so that, when you paint an image designed for them, they wrap that images colour around the 3D model to give it colour and texture. This is called a UV Map. (why UV, God only knows why geeks gave made U=X and V=Y… I certainly do not, but I digress).
So, here’s what you need to do. export your model from DAZ STudio to Waveront OBJ. Load your model in UVMapper: http://www.uvmapper.com it is free.
SAVE the Texture Map (actually, it’s a texture template) and that texture template is what you paint on.
Once you are done, you load your model into DAZ Studio, make sure it is selected in the Scene Tab, go to the surfaces tab, and under Diffuse Colour, apply your texture.
Convoluted? Yes… but then, everything 3D is…
HOWEVER, if this is already painted onto a Texture Template (and that very well may be by the look of it) all you need to do is apply it to the diffuse colour in your surfaces tab, and voyolay… instant colour JPG, PNG are good formats to use…