The manufacturer warning for the batteries:
Use only batteries supplied by SkyGolf® to operate your
SkyCaddie; use of non-authorized batteries can void your product
warranty. Your SkyCaddie may not operate properly or can be severely
damaged by using non-authorized batteries.
I found these batteries all over the web as far as retailers so a quick google search for "Skygolf batteries" and your model should bring up some options for you to pick a supplier that meets your requirements. .
To Remove the Battery:
1. Using a small Phillips screwdriver, remove the three recessed screws on the
back.
2. Gently open the rubber plug on the right side of the unit.
3. Place the SkyCaddie in the palm of your hand with the screen facing down and
the antenna away from you. With your free hand slowly pull down on the front
half of the SkyCaddie.
4. Place the bottom half (the side with the battery) on a flat surface battery up,
belt clip button down.
5. If there is a plastic bar over the battery, gently press up on the right-side of the
bar to release it. Otherwise, continue to step 6.
6. Unplug the battery and remove.
To Install the Battery:
1. Plug the new battery into the connector at the bottom of the circuit board. The
red wire goes on the left. The connector is polarized and can only be plugged
in one way. Do not force the connector in backwards.
2. Set the battery back into the battery compartment and tuck the wires along the
top, but not under the battery, so that they do not extend past the height of the
battery or raise the height of the battery.
3. Align and connect the two halves.
4. Gently press the two halves of the SkyCaddie together and replace the screws.
5. Close rubber plug on the right-side of the SkyCaddie.