You can have a Belize PayPal account to send money out of Belize but it needs to be linked to a credit card and not a bank account as we do not have ABA routing/sort codes. But you cannot receive money to it - even as a credit on the credit card. Although as the saying goes "where there is a will, there is a way", so if you really want to go down this route stop by.
I think a better alternative is AlertPay. They are truly international, so you can have a Belize account with them, and use your credit card to fund and receive payments. You also have the option of them sending you a cheque if you do not have a credit card. There is still no direct link to a Belize bank account because of the no international code problem, but at least you can receive payments from people paying by credit card and easily get the money to Belize. For more info use this link -
http://shop-4.it/euWToV