There is a roundabout way of doing it on some routes. For example to Dulles. Go to United, log on (create an account if you don't have one). Book flights, business class, non-stop, award travel, two seats and check availability using the monthly planner (look for dates with four dots). Look for non-stop flights only, and those operated by Aer Lingus or ASL airlines (also Aer Lingus in practice).
The availability that shows there is actually the Aer Lingus availability, you can then go back to avios.com then and book the flights that show on the United website. I have checked and this definitely works (e.g. business class out two seats out on March 9th, back March 17th, total 200,000 avios plus €482 taxes).
I am not sure what routes this works on. Basically you are looking for a route that United and Aer Lingus codeshare on, then this works.