6 1/3AA cells are the only option, unless you want to try fitting 6 mass plate cells into the area, which means you might want to remove more potting to get the needed volume. Pretty much any capacity cell that fits will work, though I would recommend only using NiCd cells there, not NimH cells, as the NiCd cells are a lot more tolerant of continuous float charging, which will damage the NimH cells in short order. The cells should be available from your favourite online auction site, preferably as either a set of 3 tagged cells in a sleeve, or as individual tagged cells, that you simply solder together and insulate ( especially the ends of each cell, you do not want to short them out) using some Kapton tape, and then simply pack in the space and use some acetoxy free silicone, or put the cover back on and use some thin polythene foam packing as a filler.
Charging circuit I would guess is a diode from the battery side and a current limiting resistor, giving a charge current of around 10-15mA for the pack. Probably a 560R 0.5W resistor on the board only.