you likely have a very sensitive child who feels extra remorse and guilt. If so, don't try to talk them out of it, it doesn't work, they only think you don't understand the level of their depravity. they are sensitive to the awareness of their own sin and are completely aware you don't know all the bad stuff inside of them. they don't believe they deserve to be saved.

so tell them that they are ABSOLUTELY RIGHT! they DON'T deserve it and that the sin inside is evidence of that. so instruct him to get on his knees every time he has doubts and THANK God for giving him what he did not deserve.