Is 'on', or 'to', of'of' required after the phase of ' have no problem'?

The preposition for "I have no problem" is "with."

I have no problem with getting the proposal approved.

The informal idiom is "problem with" in the sense of having no serious objection to something. This is a reflection of attitude. However, if you mean that you have the necessary votes (say) to get the proposal passed, then you would want to say "I have no problem getting the proposal approved," or better: "I will have no problem getting the proposal approved (when the vote is taken)."