I agree with you there that actual wire transfers would probably not be the best way to go, but Western Union does offer other forms of accepting online payments.
Possible things of interest on there:
Western Union® Auction Payments (send/receive online payments - U.S. + "several other countries")
Western Union® MoneyZap (send/receive online payments - U.S.)
Western Union® Phone Pay® (take check payments over the phone - U.S.)
Western Union® Quick Collect® (receive payments online or from Agent locations within the U.S.)
Western Union® Quick Pay (receive payments from Agent locations outside the U.S.)