Both “she said goodbye too many times before” and “she had said goodbye too many times before” are grammatically correct English. They have slightly different meanings.
I suggested rephrasing prior to translation, to clarify the tense of "said".
As someone upthread noted, it's a song, so prosody is more important than grammar. But I think it's still an ugly construction.
[Edit] I'm not sure what tense it is; I'm a native English speaker, and I don't think I was ever taught the grammar of my own language. I don't think it's past-perfect/pluperfect; that would be "she has said" (she has finished saying it). Wikipedia disagrees, but doesn't say what tense "she has said" is.