Rather than using a standard ELO, use the net number of coins a player has won as the measure of their skill.
If the goal is to prevent players from artificially lowering their ranking to gain coins, then tie their ranking to the number of coins they have. While abuse is still possible to a limited extent, it's capped at the number of coins you can earn in a single game, because as soon as they start to have any success with their plan, their ranking rises. It's a self-correcting system, just like a good ELO system.
If you want to aggressively encourage players to pair against people of the same skill level, then set up a ratio system in the bidding, so that one coin from a player who has very few coins matches ten coins from a player with many coins when bidding - this discourages players from playing against those with significantly fewer coins (because the rewards are less and the risks are higher), and means the players who do well against higher-ranked players will advance quickly. This mimics the ELO system of scaling rating changes based on opponent's strength.
Coins gained from alternative methods (buying coins with real-world money, promotions, etc) shouldn't be factored into the ranking, only coins "earned" during play.