Transcontinental flat-bed flights on UA - How do I find them?

I am planning a family vacation in paid J, and most of the flights I am looking at through EWR or IAD (from SFO).

Sporadically, I come across a 767 or a 757-200 (flat bed) configuration or even a 777 but it's not on a regular schedule/

What is the best way to find dates and routes that have flat beds for SFO-EWR or SFO - IAD (and vice versa)?

Any tools that I should look at or is it trial and error?

Any tips would be appreciated!

Thanks :)