As I have posted elsewhere, this and a plug and a thermistor, the latter two being easily harvested from a dead battery (there must be some of those still about), will do the trick about as well and as cheaply as it can be done. An alternative is a 4xAA plastic battery holder wired to the male connector internal to the eMate. Even alkalines would run it in intermittent use for a long time, and you would not then need a charger at all. Those are expensive.

The general arrangement is here; battery holder hacks can be found if you go looking.