* "After a long day in the dusty hayloft, his eyes were rheumy and red."
* "The baby's rheumy eyes made it hard for her to see."
* "The cold weather and wind made my eyes rheumy."
You can also use it figuratively to describe something that's damp or misty:
* "The rheumy air hung heavy with the scent of pine needles."
However, it's not a very common word, so be sure the context is clear when using it.