This depends on how you define 'rhyme'. A pure rhyme is a word which rhymes with each syllable of the other word with which you wish to rhyme. If this is the case, I'm afraid there are no pure rhymes for the word autumn.
There are however over 800 of what are called 'end rhymes', where the final syllable of 'autumn' rhymes with the final syllable of another word.
Some examples of 'end rhymes' with 'autumn'
One syllable words:
Chum, dumb, glum, gum, crumb, come, drum, hum, mum, come, rum sum, thumb, swum, dumb, numb.
Two syllable words:
Album, blossom, boredom, denim, emblem, fathom, fearsome, freedom, handsome, loathsome, phantom, problem, stardom, victim, wholesome.
Thee syllable words:
Buddhism, cherubim, cuddlesome, cumbersome, martyrdom, maelstrom, meddlesome, nudism, sarcasm, quarrelsome.
Or, you could try using 'fall' instead of 'autumn'!
Perhaps this reading of Keats' 'To Autumn' will inspire you:
