I used the same method as for Neptune, using my old data from last winter. The result is at http://www.finerandd.com/astronomy/Uranus_circular_orbit_method.pdf (http://www.finerandd.com/astronomy/Uranus_circular_orbit_method.pdf).
The basic assumption is that Uranus and Earth follow coplanar, circular orbits. I compare its position against catalogued stars as it moves through the heavens; and do some geometry.
Uranus is quite close to its aphelion at the moment. I got the distance pretty well smack on the distance at the last opposition, and my predicted opposition time is 11 hours late. Because I have calculated a period based on what is essentially the aphelion distance, this period is a bit long.
It's actually 84.3 years. My dad turned 84 this year, so I surprised him more than slightly by sending him a "one year old" birthday card and explained that he is one Uranian year old.