I can't comment on the PO box situation in Caye Caulker but in San Pedro they are like gold dust and there are a couple of private companies providing boxes. But with or without a box, the PO are customs brokers and will clear parcels for you. They will put a notification in your box (one of theirs or a private one), or just in the cubby hole for your surname initial inside the office. When you go to collect they will open the box to make sure it is what it says it is, calculate the duty, GST, etc and you pay them direct. They charge just 75cents belize for this.
But, many online companies will not deliver to Belize and if they do they will try and use a courier company like Fedex or DHL as there seems to be a general distrust in the US of the post office and international delivery. My personal experience is that the post office is the best option, especially as they have offices throughout the country and on the cayes. To solve the problem you can setup a US mailbox, have everything sent there and they will then consolidate it to save on postage and forward it to Belize. I would recommend these guys -
http://bit.ly/eMLixi - as you can track everything on line, their prices are good and they are super helpful/friendly. I have used them for ages and never had a problem.