So, the battery on VS goes into a MB8416, as through a 100r resistor to CS. (the bit with the transistor operates as open while the normal PSU is at 0)
According to the datasheet, the 8416 will hold data down to 2.0V and operates normally at 5.
As the battery is going to through a silicon blocking diode, it drops about .7 volts.
We want the IC to have at least 2v, so we need 2.7v (at least) 3v seems good, but we can go up to 5.
The classic combination of 3 AA's in series gives 4.5 at full charge, and should give a good live.
A 3V coin cell would also work, but might not last as long.
As for battery life, the IC's Datasheet states that it draws 10uA when in stanandby.
A CR2032 has a typical capacity of 240 mAh (until 2v). Which means it should last about 2.5 years.
The A91(aa) battery datahseet does not give figures for discharge at such a low current, so I'll use the lowest one of 2500 mAh at 25mA so if, which gives us roughly 20 years, but we all know that other factors tend to break that (leakage current and other goodies).
Typically, AA's will only last 2-5 years in similar situations.
http://www.johnsarcade.com/vs_downloads/misc/VS_Schematic_%28MDS-02-CPU%29.pdfhttp://matthieu.benoit.free.fr/cross/data_sheets/MB8416-20.pdfhttp://data.energizer.com/PDFs/cr2032.pdfhttp://data.energizer.com/PDFs/E91.pdfTL;DR
A 3v coin cell should be sufficient, but the classic 3 AA's in series will give you more life, probably.
