Oh, so he can't transfer a ps4 save to my system through battlenet?
Nah you should be able to do that by logging in as a guest user with his PSN account and allowing his save to sync up. Battlenet isn't involved with that.
But you can I my have I've account logged in at a a time for local coop so either you'd have to play on his acct or he'd have to play on yours. It doesn't support two account logins at one as far as I know