While skimming through magazines, I found Tony DiStefano's article on the
subject... here are the relevant details:

Upgrading a 16K Color Computer 2 to 64K
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Open the case by removing the screws in the
bottom, then carefully remove the keyboard.

Remove the eight identical chips located
along the front edge of the CoCo2 main board.
These are the 16K chips.

Replace the 16K chips with 64K chips. There
are many different part numbers which will work,
as long as they are comatible with 4164 chips.

Look for a small "W1" in between the 6822 PIA
and the 74LS244 chips. Right above the "W1" mark
are two solder points. Solder these two points
together and re-assemble the CoCo2.

You now own a 64K Color Computer 2.

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Some hobbyists used to piggyback the 16K chips
to get 32K of memory. In the mid-80's that might
have been a good choice, but I wouldn't recommend
it these days. If anyone wants the instructions
to do that, I can provide them.

Note that the CoCo2's 16K chips are 2118 chips.
4116 chips will *not* work in the CoCO2.

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Source: Tony DiStefano, Turn of the Screw
The Rainbow, January 1984, p.130