There are a couple of plug and play options to run Nintendo boards in JAMMA cabs, but I haven't seen one that goes the other way.
About as close to plug and play as you're going to get is to remove the innards from the one side, drop in a normal CGA monitor, power supply and JAMMA harness.
Otherwise, you have to deal with the difference in voltage (Nintendo ~ 100V), video inversion and amplification (Nintendo is amplified off-board, JAMMA is on-board) and wiring harness (I am assuming that you're running a Dualsystem board rather than two Unisystems). I don't think it is as clean a solution as you are looking for.
If I were you, I'd grab a different VS kit to replace the Dr. Mario.