If you mean like Interact, yes, but not every seller is set up to accept them.
If you mean like wire transfers, which are popular in Europe, yes, but most North American sellers are unaware of them. Those that do know what they are will probably refuse because North American banks charge $25 or more to process them.
The seller must offer only payment services which can be electronically viewed by eBay.
Buyers can offer any sort of payment they like, BEFORE bidding. Sellers can accept or refuse.
A minor exception. When a purchase is completed on pickup, the seller can demand cash payment, but only in this case.