My front calipers are Girling, can actually read it. BUT I really need
rear calipers, and need to identify them to make an order. They are ATE and
there is numbers of 52.....G on one side and 19.....G on the other. So I'm
hoping someone out there can tell me if this means 36, 38, or 40 MM. Thanks.

There should be a little round-ish area, machined off smooth, with a number stamped on it. See the photo in this excerpt from the 700/900 FAQ (Caliper Identification):

https://www.brickboard.com/FAQ/700-900/Brakes.htm#BrakeCaliperIdentification
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Current rides: 2005 Volvo S80 2.5T, 2003 Volvo V70 2.4NA, 1973 Volvo 1800ES (getting ever closer to road worthiness)

I definitely do not see the machined off smooth area on mine. I guess
too much rust. I'll have to try to get the imprint on the back of the shim
plate, which I was avoiding because I didn't want to take the rusty parts
out and hope to replace them while I'm waiting for the right caliper.
Oh well that's the only solution.

In the progression of the 700/900 series the later calipers were usually 40mm,and your rear calipers are most likely to be 40mm. You could get a pair of 40mm rear calipers, and install them. You'd know that you'd have a fresh matched pair.
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john

I took off the shim and measured the diameter of the piston mark, apparently mine are 36mm. I assume that you need to buy the same calipers because the mounting points are different, correct?

The mountings are all the same. You can install a matched pair of calipers of 36, 38, or 40 mm.
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john