Actually singing the track twice is my favorite method because it sounds so different from the delay tricks that were previously mentioned.

But if you come to a certain passage or phrase that just doesn't double well because of your vibrato, you could simply add delay to that particular passage only. Wherever there is an offensive part, mute the second vocal track and add in a track of very tight delay. Should work pretty seamlessly.

http://www.soundclick.com/MarkKaufman