Yes, but not without taking your iRiver apart and voiding its warranty. The H300 series has no official support for battery replacement, which is a feature of other players such as the H10.
Replacing the iRiver battery with a higher capacity aftermarket battery
The iRiver H300's battery has been successfully replaced with an IONITY LiP385585, giving a new battery life of over 25 hours of MP3 playback.
Installation of the IONITY requires disassembling the iRiver. While this process is reported to be relatively simple, it could potentially damage the player and will unequivocally void its warranty.
More information, including battery tests and purchasing details for the IONITY battery, can be found here:
Done It! IONITY LiP385583 runs in H300 Series