Hi @mikeadams ,
If you can't find the correct replacement battery try the following to hopefully find a compatible battery for the speaker:
Measure the dimensions of the battery in mm (millimetres), i.e Height (depth) and Width and Length
Then write the results as in the following example,
H = 5mm , W = 60mm, L = 85mm , the resultant figure is 506085.
The first 2 digits are the height and the convention for battery sizing is that there is a decimal point between them, not shown. The next 2 digits are the width and the last 2 are the length, all in mm. Obviously if the battery has a measurement longer than 99mm then it is three digits.
Once you have the number search online for a 3.7V 600mAH (insert number) LiPo battery and check the results. If there are none go for one that is as close to (just under) the measurements as possible especially with regard to the height.
Getting a battery which has the same (or just under) dimensions as the original will ensure that it will physically fit into the speaker
Ensure that the voltage rating of 3.7V is the same. The capacity (mAH) doesn't matter if it is greater as this means that the speaker will stay on for longer, but it also means that it will take longer to charge.
Hopefully this makes sense and is of some help