Hi Henry,
I haven't been able to successfully use bone or skin weighted animations with DarkBasic Classic. It does, however, support articulated structural animation pretty well.
Basically, you would have one object made up of several different meshes. They are NOT tied together by armature or bones, but by parent child relationships or limbs. You animate the object by moving each limb a little bit and and setting a keyframe.
I think a lot of 3d software use this technique for animating an entire scene. All the objects in the scene get placed at different positions and keyframes are set. If you can export a directx or 3ds file from C4D that is an animated scene, you might be in business. I don't really know because I have never used C4D.
Though you'd essentially be using a scene to create one character in DBC. I'd actually be curious to hear if that worked! I almost got it to work with a program called Anim8tor, so I know in theory it is possible.
I hope this is helpful.
Enjoy your day.