For folk music,if all else fails, try going with the poetry of the lyric rather than struggling to get the melody exactly right. Speak the words of a song out loud over a simple guitar accompinement a few times before you start singing . If neccessary alter the tune to fit your voice and , to that end , cultivate your speaking voice .I think it was William Blake who said " A bird never soared too high that flew on its own wings"
Bear in mind that there will always be one song that you really like that you won't be able to sing . For me it's Ewan Macoll's Travelling People - the last word of every verse just throws me for some reason.