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You don't really need to remove the tray to cut the holes. I used an Irwin #22 micro- dial expansive wood bit (see picture) adjusted to 2 7/8". I would think you could use any hope saw of that size. The only trick was finding the exact center before cutting. I did that by cutting a test piece out of scrap formica (you could use any thin wood-like material), then placing it down in the cup holder. I've ordered these inserts which I believe will fit perfectly into the holes: Plastic 2 7/8 Black Cup Holder https://www.amazon.com/dp/B00MMRKRXO/ref=cm_sw_r_cp_apa_W0Fsxb6YTT6J2
I bet you could also cut the holes by hand with a coping saw. The holes don't need to be perfect if you're going to trim them out with drop-in cup holders. Just disassemble one end of the blade from the coping saw frame, stick it through a pilot hole, then reassemble and cut.
I inherited that "expansive" bit many years ago. I think they call it a "spade" bit now. I think this would do the trick:Irwin 44202 Lockhead 7/8-Inch to 3-Inch Adjustable Spade Drill Bit
That should read "any hole saw of that size. "