Amateur astronomers discover new comets all of the time. But what is with kuiper belt objects? Short period comets (less than 200 year orbits) comets originate in the Kuiper Belt, located inside and outside of Neptune's and Pluto's orbits like Kuiper belt objects. But comets have very eccentric orbits so they come in interior part of solar system and then they become brighter so amateurs could discover them (the most comets discovered by astronomers amateur at the moment of discovery have apparent magnitude about 10-15 where smaller number means brighter object).

Kuiper belt objects have less eccentric orbits and approximately constant distance from Sun so and their apparent magnitude is constant ,magnitude of brightest objects is about 20 and that is greatest magnitude that the most astroamateurs could achieve with their telescopes. For several years now, astronomers have studied the farthest reaches of our solar system only using the full sensitivity of large professional telescopes on the ground without help from amateurs. These professional surveys mostly seek for kuiper belt in plane of ecliptic (plane of earth's orbit and of most other object in solar system). But there is trans-neptunian objects with highly inclinated orbit so there is chance for amateurs to discover brigher kuiper belt object who have high angle from ecliptic. But I think that amateurs don't use that opportunity