well for tiny (1/8") and standard (1/4") eyelets, nothing beats the Crop-O-Dile found in the scrap book section of any craft store. It has leveraged punching motion, so it doesn't tire you out with lots of use. It punches holes and sets the eyelets in darn near any material: paper, chip board, leather, plastic, thin wood, fabric, even thin metal sheets like copper & brass. I have the Big Bite version with a 6" deep reach, it ROCKS! Yes, it costs a bit (about $40 US), but so worth it if you do a lot of eyelets and/ or hole punching. I've made a dozen corsets with mine and it's still going strong.
I've seen a foot pedal operated machine that does the same thing but for large grommets (in the 3/4" to 1 1/2" range), but it was a commercial thing at a flag company. I've never seen anything for home use that was anything other that the mallet & punch set available at hardware stores.