Can someone who has done an Aveira pay someone to transfer the punishment to him?
A few thoughts - The Gemara brings down that when Moshiach comes Yitzchok Avinu will end up saying Palga Alai - I will take half of Klal Yisroel's sins upon myself. Can this be a proof that sins are transferable?
In addition if an Aveira could be sold - who would do teshuva on it?
There is a source for transferring a curse. When Rivka tells Yaakov "alai kilelascha bni" (Toldos 27:13), some mephorshim translate this literally. For example, Seforno proves that you can accept someone elses curse from Shlomo Hamelech who accepted Yoavs claim that he cannot get both Dovid's curse and death, so Shlomo accepted the curse and then ordered Yoav killed (Sanhedrin 48b.)
Others do not go with this interpretation. It is unclear if they differ with the above concept.
Either way, there is a difference between transferring a curse and transferring a sin or the related punishment. I thought the above might be helpful.