Order the Dayton 12" sub, put it in a corner and make sure it's a few inches off the ground, and build a small 3' x 3' shingle roof over it. You have to protect it from rain, and I'm not all that certain it will survive the condensation and heat of summer.
The electronics in the amp could corrode, and the moisture could ruin the mdf box, or at minimum affect the sound. Your only other option is to build a box out of pvc, and silicone the heck out of the box to make it weather tight (acoustic suspension design), which means you'll need a larger amp - preferably placed inside the building. And after all that, it still may sound like dung due to placement issues and lack of walls.
BTW, why are you looking for bass outside?