Aliexpress sell a compatable battery,
Search "Original 250mAh SP551923AE Battery For Pebble time steel Smart Watch Batterie Accumulator Akku"
US $6.99 / piece
with the control cct on board, you just need to solder to the edges of the existing copper pressure pad ( cut the old battery and lead away) and it works well. It says that it needs a good 9 hours charging for the first 2-3 times.
After cleaning the old glue from the body and screen, I asked a phone repairer at the local shopping center to glue it back......He passed me the glue and said you do it and it's free.... If I do it, I charge you, so I did a light bead and kept it clamped for 24 hours and it's great. I turn it off every night and I get about 14 days.