Your bankruptcy will have no impact on his credit rating unless you had any joint debts in the past (unlikely though given his age).
It may be because he has never had any credit before. Which banks has he tried? Barclays and Nationwide are a couple to use otherwise there are banks that have paid for accounts such as Thinkbanking, Secure Trust and Clearcash. Guaranteed acceptance just has a monthly fee.
As Niobe has said, it could be because of his own credit rating, but as he's only 18, I should imagine if he can prove his address, he should get an account.
The Co-op are a good bank, did they give him any reason why they rejected him?
Is he on the electoral roll? If he is but has only gone on recently it might be the case that the credit files haven't been updated to show this yet. I got married last September and the electoral roll wasn't updated to show my married name until the end of January.
The more I have to do with humans the more I think that the world would be a better place if it was run by animals.
Last IPA payment made on 28th June 2010 and I'm now looking forward to getting married in September 2012 - I'm proof that you can go BR and come out the other side.