instead of singing the song sing the root of the chord you are playing over. after you can do this what you do is sing other notes in the chord when you play it, eg the fith or third. this should allow you to choose these notes. now what you do is when a there is a chord change sing the root note, then sing some other notes in the key, notes in the chord should be easier.

also start with sinple rythms although make them more complex as you progress.

overall this should help you sing and keep in tune. at least it worked with me.