Neo 1973 Battery
The battery is a one 3.7V (nominal) cell. It has internal protection circuitry, and a capacity of 1200mAh.
On the battery, which has dimensions of approximately 53mm*38mm*7mm is written "FIC, First International Computer, Model: GTC-01/GTA-01, Standard Battery Pack, 1200mAh Li-ion, Rechargeable Battery: 3.7V".
It is apparently compatible with the Nokia BL-5C See this mailing list post These are available very inexpensively from ebay. Though quality will of course vary.
BL-5C battery will work in Neo, but not the other way around. Battery is too thick for Nokia, and attempting to use Neo battery in nokia will result in Nokia entering strange "test mode".
Nokia BL-6C is a bit thicker than BL-5C, but (almost?) identical in all other dimensions and electrically. Maybe it'll fit inside Neo too. The original BL-6C is 1070mAh compared to BL-5C 850mAh making it a slightly more interesting replacement battery. Could somebody confirm if it fits?