If you go to Lowes, they sell black (and clear) plastic sheet of 4ml and 6ml thickness, its perfectly adequate for a small pool, if you had any doubt about its ability to be durable, you can always put two layers down. It's on a roll, 10' x 100' about $15 and $25

Birds landing hard on it might puncture it, however with careful protection its no biggy. At that price, its fairly easy to re line it in future years....

Regards, Andy