In vanilla Civ V I wish to play a game with a friend where he makes the troops and I support him with money. I am curious as to which civilization will help me make the most money.
In vanilla Civ5, I would probably suggest the Arabian civilization, as their trait (Trade Caravans, +1 gold from all trade routes) and special building (Bazaar, increased luxury resources, +2 gold from oasis and oil tiles) both increase gold flow.
However, it's possible to be filthy rich as any civ. Just make sure you prioritize techs and build stuff that increases gold flow. For instance, make sure you get Markets (or Bazaars, if you play as the Arabians) early.
You also want to focus on building Trading Post tile improvements wherever you can.
Try to avoid building things that you don't need in your cities which cost gold per turn. For instance, if your friend will be supplying you with military units, don't build Barracks in every city.