I think the alternator you cant change, and a bigget battery would be a idea, but the fact still is your alternator can't handle the load, and its a starting battery, not a deepcycle. You will still have your problem unless you have a bigger alternator or find a small atv deep cycle that no one makes.

 

iv been looking at one of these 2 batterys. but the price i dont wanta pay.
Price Range: $106.95 - $124.95
SPECIFICATIONs
Product ID: YB30L-B(MotorCycles)
Cold Cranking Amps: 300
Voltage: 12
Weight: 14.1
Width: 5.19
Length: 6.63
Height: 6.94
CYCLE-TRON HIGH PERFORMANCE - 300 CCA - 30 AH
High Performance conventional 12-Volt batteries are available with and without an acid pack. Lead calcium technology means the high performance conventional generates more power, requires less maintenance, and lasts longer than any other conventional battery. The conventional battery gives you a powerful advantage. Its high technology separators allow two extra plates per cell to be installed, for a 30% improvement in cranking performance
or
Price Range: $154.95 - $180.95
SPECIFICATIONS
Product ID: FAYIX30L(MotorCycles)
Cold Cranking Amps: 385
Voltage: 12
Weight: 22
Width: 5.00
Length: 6.56
Height: 6.88
CYCLE-TRON PLUS - 385 CCA - 30 AH
Interstate's Cycle-Tron batteries are fully charged and ready to use. Along with Absorbed Glass Mat (AGM) technology, the batteries come from the manufacturer completely charged and sealed and can be mounted at virtually any angle without spilling, leaks or water to check. JUST PLUG AND PLAY!!!

 

Interesting that they are both 30AH but one is 14lbs and the other is 22lbs. Weight is usually a good indicator of a battery's capacity, but from my experience, the sealed batteries are usually less efficient in that respect. You need a battery with the most AH rating. Big CCA is good but I doubt that there is a cable on your bike (conductor) that would take 300A for very long let alone any need for your starter to draw that much current.

That is a lot of money for a LITTLE battery.

You may be able to get by for your short trips if you hook up to a battery charger when you park it.

 

I am using the gel filled batteries lately and they seem to be a much better battery at about the same price as the wet ones.