Perfect Rhymes (same vowel and ending sound):
* There aren't any true perfect rhymes for "ergonomics" in the English language.
Near Rhymes (similar vowel sound, but different ending sound):
* Economics
* Harmonics
* Phononics
Eye Rhymes (spelled similarly, but pronounced differently):
* Chronics
* Tonics
* Ironics
Other options:
* You could use slant rhymes which have a more distant connection in sound, like:
* Logistics
* Statistics
* Diagnostics
Ultimately, the best rhyming word will depend on the context of your poem or song.