i have find a 3600 3600mAh battery, it said that it's Capacity more than three times of your original battery.
original source:
http://www.gogamestuff.com/gogamestuff-topseller-skuid-a06092900ux0062-brandid-3-typeid-29-detail.html

another source of new type psp 2000 cover for the fat battery

After see this helpful article, i seach "psp battery cover" on google, find a new type psp 2000 cover for the fat battery (1800 mAh).

One site is sourcingmap, a wholesale site, the price is $2.99, and the shipping fee is $5, but the price will reduce if you buy more than one. the url is: http://www.sourcingmap.com/black-replacement-battery-door-cover-case-for-sony-psp-2000-p-11857.html

Another is gogamestuff, the price also $2.99, but if you buy additional one, the shipping fee just need $2. the url is http://www.gogamestuff.com/gogamestuff-productsShow-skuid-a07121800ux0010-brandid-3-typeid-29-detail.html

Here is just what i found on google, if anyone find more useful site, please share with us.

Thanks, but one thing, many people may throw away their fat batter (1800 mAh), for buy a new one need more than $20.
So i like to share what i found.

I have saw a new type of psp 2000 cover for the fat battery (1800 mAh) somewhere,
The cover for PSP 2000 thick battery is designed and developed for PSP 2000 console and can be compatible with PSP 1800mAh battery, which can effectively extend PSP 2000 console using time and is convenient for the players who could not buy new batteries. After inserted PSP battery into PSP 2000 covering the battery cover, can effectively prevent the battery off, Simple but practical.

The original source:
http://www.gogamestuff.com/gogamestuff-productsShow-skuid-a07121800ux0010-brandid-3-typeid-29-detail.html

Good job, but one thing, many people may throw away their fat batter (1800 mAh), for buy a new one need more than $20. So i like to share what i found.

I have saw a new type of psp 2000 cover for the fat battery (1800 mAh) somewhere,
The cover for PSP 2000 thick battery is designed and developed for PSP 2000 console and can be compatible with PSP 1800mAh battery, which can effectively extend PSP 2000 console using time and is convenient for the players who could not buy new batteries. After inserted PSP battery into PSP 2000 covering the battery cover, can effectively prevent the battery off, Simple but practical.

The original source:
http://www.gogamestuff.com/gogamestuff-productsShow-skuid-a07121800ux0010-brandid-3-typeid-29-detail.html

A source of Pandora Battery for Sony PSP
After read this helpful article, i try to seach"Pandora Battery " on google, and i have find some source which sell this battery,
one is gogamestuff.com, here is ther url:
http://www.gogamestuff.com/gogamestuff-topseller-skuid-a07122700ux0001-brandid-3-typeid-29-detail.html

It said"Using the magic memory stick and the magic PSP battery you can Unbrick& Downgrade any PSP easily."

Another site is uxcell.
Here is just what i find on google, any one have other source , please feel free to share with us.

A source of Pandora Battery for Sony PSP
After read this helpful article, i try to seach "Pandora Battery" on google, and i have find some source which sell this battery,
one is gogamestuff.com, here is ther url:
http://www.gogamestuff.com/gogamestuff-topseller-skuid-a07122700ux0001-brandid-3-typeid-29-detail.html

It said"Using the magic memory stick and the magic PSP battery you can Unbrick& Downgrade any PSP easily."

Another site is uxcell.
Here is just what i find on google, any one have other source , please feel free to share with us.