Hi -- I'm a former kindergarten and current pre-K teacher, so I have a few ideas. First of all, you should know that rhyming is part of the area of pre-reading skills known as phonemic awareness, so you can google that for ideas, or look at a teacher store for books about phonemic awareness.
One thing to do would be to read a lot of poems to him (silly ones like Jack Prelutsky's would be fun), recite nursery rhymes, and sing rhyming songs with him. Then play a game where you say a familiar poem/song and get the rhyming word wrong -- "Jack and Jill went up the mountain" -- so he says, "No, Mom! Went up the HILL!" and fixes your mistake.
Another would be to start rhyming some words and have him jump in with more, remembering that nonsense words are totally fine: pail, mail, bail, fail, gail, rail, sail, nail, zail, yail, lail, etc.
You could also write simple rhyming words in a column so that he can see that the ending letters are all the same, and then can make his own by substituting the first letter. (-an, pan, can, fan, etc.)
There are rhyming picture cards you can buy at a teacher store to use so that your son has to sort the pictures into pairs of words that rhyme (boat/coat, mug/bug).
Hope this helps!