Yes, all if not most of the MPs will rent out their rooms to couples, no matter what the circumstances or their profession. Just pay their published fee and there should be no problem. After all, it's just extra income for the house, and most of them are suffering a little bit these days. Call ahead of time though giving them a couple of hours notice to ensure availability. You might want to have a backup, in case business ramps up when you get there.
Typical room fees are:
60min - $50
45min - $40
30min - $30
Multiples of these are negotiable...