I'm gonna go ahead and assume that COCOnut means "but" Also the last line of your questions says you dont want to speak with a live person OR a recording. So there is actually no other way to transmit information. So I'm also going to assume that you DO want to speak to a live person. In which case you can just keep pressing 0 to get to a representative. Although there is a voice prompt specifically for reporting a payment.
Though dennis is right, you don't need to report payments unless your service is disconnected.