GBC & GBP | How long will the CleanJuice last?

This will depend on the console you are using and the upgrades you have.

Game Boy Color

Since the GBC uses the same battery as a Game Boy Advance, you can expect the same life expetency as seen in this article in the GBA section.

Game Boy Pocket

The GBP has less of a power supply than the other consoles. You can expect around 2 to 3 hours on a console that is modded with an IPS kit and other mods that draw power. Use of an EZ-Flash or similar, will significantly reduce the battery life.