I think the ball bearing might not be necessary, if your tray is small enough to get complete rotation by hand. But in case you need one, what I did is just route a concentric 1/8" flat-bottom groove in the bottom plate (of HDPE), making a circle about 5/8" in diameter and about 123.5 mills deep after debur/polish, then drop in about 8 or 9 1/8" steel balls. It will spin for a good few minutes. Easily > a full rotation with a flick of a finger. All done with simple router table and a nail. But you will need a small clearance plate to get the circles that small. The hard part was the deburring.
Another method that worked ok was to route the entire surface of the bottom plate away, by just a few mils, except for a small sub 3/8" diameter circle of HDPE in the center and a small rim around the outer edge. Then route away most of that outer rim so it's just a series of evenly spaced nubs. Then sand down the nubs with 400 grit to round them off and lower them by a mil. A little graphite on the center bearing area, and it spins ok. Just good enough in this case, but kinda meh, really, compared to the ball bearing. The nubs are there to prevent excessive tilt when you press on the tray, of course. 1/8" nail for the axle.
Practically, I think tray maybe needs to be larger than 3" diameter (or made of heavier and higher tolerance material for a smaller tray), for such crude bearings to work, though. For the rotational inertia. Hopefully, you don't need to go there. Heck, you might come up with a better solution for a tiny tray, like a gear or banded pulley system with a separate knob.

Also, thx for keeping an open mind. I think it could be good. Always thought there was too much going on with the right hand with these manual PnP machines.