What kind of battery does the Pokémon Go Plus have?

According to this article (specifically, point 13; "Do I need to charge the Pokémon Go Plus?") the battery inside is a CR2032 lithium coin cell. The Plus's battery life is estimated at 100 hours of use, so if you use it frequently - start stocking up.

I have had my Go Plus since day one. The battery is indeed a CR2032 coin battery and my experience of using it most of the day, is that your new battery will need replacing every month or so. If you don't use it as much it will last proportionally longer.