There are many words that rhyme with "him". Here are some examples:

• 1 syllable: dim, grim, gym, limb, rim, slim, swim, Tim
• 2 syllables: begin, chimp, hymn, krim, prim, skim, synonym, trim, whim
• 3 syllables: cinnamon, discipline, mandolin, violin
• 4 syllables: acetaminophen, phenylpropanolamine

Note that some of these words may not be suitable for all contexts, such as "phenylpropanolamine", which is a chemical compound.