Has anyone made GBA SP extended battery that fits in the SP's original battery compartment without sticking out?

I think, the GBA SP uses a 3.7V 650mah battery.

I don't have a DS lite at the moment but *I think* it uses a similar sized battery, but with 3.7V and 1000mah. I wonder if that could be modded to fit in the GBA SP? Maybe a cellphone battery would be a better option?

The DS Phat battery will fit with very minor modifications. You'd have to clip off some plastic, but it fits perfectly, and charges perfectly. Mine's marked for 850 mAh. A DS Lite battery would require some more modifying. You'd have to peel the plastic housing off completely, then rewire the contacts to the end of the battery. If you do that, the width should match an SP, but the length might still be a millimeter or two short. There are loads of phone batteries out there, your best bet would be to use the dimensions of the SP battery and see what's close.