sure mekako,
I think these replacement batteries are better quality too, my player just ran for 13 hours non stop!
The battery size is posted above and here is the link to the EBay seller I got it from.
Ipod Mini Battery
I did have to cut the connector off and solder it in though.
It would be a good idea if there was a section on this site just for batteries and power supplies as the information seems to be all over the place.