The problem might be to get a battery with the appropriate connector to fit the existing battery connector on the board.
Measure and write down the height then the width then the length of the available space all in mm e.g. a space of 5 mm H x 62 mm W x 75 mm L would be written as 506275. The convention is that there is always a decimal point between the first 2 digits (which is always the height or depth) so it is actually 5.0 x 62 x 75 (if the space is wider or longer than 99 mm obviously it would be 3 digits for the number).
Search places such as Ebay and AliExpress for a (insert dimension number) 3.7V LiPo battery and look for the one nearest the size you want, which has the greatest capacity (mAH - milli Ampere Hour). (I’m assuming that it requires a 3.7V battery for correct operation)
Make sure that the battery that you select is either exactly the correct size or slightly under, especially in height, as you want to be able to close the iPod case.
Hopefully this makes a bit of sense.