No you can't, You would have to buy either an original or fake charger. Home made chargers would not work since the PSP requires a specific connector and circuitry.
Yes you can make a PSP charger at home but for that you would need a Power cable with 4.0-by-1.7 mm adapter plug, a usb cable and some tape. You will first need to cut these wires and join them to each other, other that this there is no way.
Unfortunately, no. in less you're an electrical engineer, it would be best to buy one. You see, making your own would be very risky, too muck power running though the charger would blow out your PSP
