Unfortunately, the late payment is a fact in your credit history, and neither the bank nor the credit reporting agencies will likely remove it upon request. (It appears from your question that you have already asked.)
The late payment will fall off the credit report in seven years.
Before then, as time goes on and you pay your bills on time, this one late payment will become less significant on your credit score.
One thing you can do before then, if you want, is to write a letter of explanation. This is a 100-word-maximum statement that will be attached to your credit report. In it, you are allowed to explain any negative items on your credit report in any way you see fit. It will not affect your credit score at all, but if a future lender looks at your report, they might read your explanation.
However, I've read different opinions as to whether or not such a letter can actually help. In your case, saying "I applied for credit for someone else, and he stopped paying" doesn't sound to me like a story that would reassure a lender that it won't happen again, unless perhaps you also say that "I realize now that cosigning for someone else is stupid, and I will never do that again." You might be better off just leaving it alone, learning your lesson (never cosign or buy something on credit for anyone), and waiting for the score to improve on its own.