He has applied for many personal and relationship banker positions. He's assuming that he's not hearing from them due to the fact that he doesn't have enough banking experience.
Has he tried applying for a personal banker position? It's probably not as commonly advertised as teller positions, but he might be more likely to get an interview considering he has prior relevant experience and he does hold a college degree.
My brothers wife is an assistant branch manager for one of the larger banks in our state. We haven't contacted her about this because we live almost 2 hours away and figured that it would be a bit far for her to have much influence.
I don't know how large his family/friends social circle is, but if he hasn't already, I recommend he let everyone know he's looking for work, particularly in the banking industry. Not all jobs are advertised online and he might have more luck following up with word-of-mouth leads.