query: a poem that sincerely apologises to a friend for rejection her

Although I don't know the specifics of this situation, let me go out on a limb and suggest a poem apologizing for rejection (whether it be romantic or some other kind) is unlikely to smooth over the situation. Unless you regret your "rejection" and now want to get with this friend. People write and share poems to make other people want to have sex with them. If that's not what you're trying to encourage, don't mess with the powerful, uncontrollable lure that is poetry. You might hurt yourself.