A little bowl of oatmeal with bananas and cherries is working wonders for my REM sleep. I will soon write up an articel about that myself. My REM percentage went from average 10-15% to 25%+ just by eating oatmeal and following a strict bedtime routine. But what is even more important are the foods that block REM sleep! Always try to eat something light at night! And avoid drinking alcohol. Just one beer at night is already killing REM sleep for me. But that depends on the person.
ps.: I monitor REM sleep with my FITBIT.