I was wondering if the sunny buddy on spark fun can be used in order to stop the battery from receiving charge once the battery has been fully charged. If this is possible how can it be done and if it is not what other components can I add to my circuit so that this action is possible.
The data sheet for the chip used in the Sunny Buddy, posted on the product page, explains the charging action in some detail.
You should understand the behavior before attempting to modify the circuit.