Of course you'd think that if sing modified to sang, bring would similarly go to brang - and the form does exist in the dictionaries, but as obsolete. "songs she brung to me" would be close enough.

I think the rule of thumb is, unless you are using the rhyme humorously, you should never sound as if you are using a word or a construction as a way of getting a rhyme. It should sound as if, just by fortunate chance, the words you needed to use to convey the meaning happened to echo each other at the right places.