Opossums like tight, secure spaces, with small entrances to protect them from larger predators. You can place an old dog carrier crate (found at garage sales or placed at curb for trash on trash days) and remove the front door from it.
Place an old rubber door mat (or purchase a length of rubber matting from Home Depot) atop the carrier to keep water from coming in the air holes
Place the carrier facing towards a solid object, wall or fence (turned outward for the photo) in the corner of the yard. Use two concrete blocks to keep it elevated off the wet ground with just enough room to squeeze up and into it. Lay down some flat newspapers in the bottom, then stuff it 3/4 full of crumpled, clean newspaper.
The opossum will rearrange the crumpled newspapers to its best advantage for warmth, privacy and protection. It may add twigs, plastic bags, leaves and debris found in the area and actually seal itself in using the material as a barricade/door. Check and replace soiled or damp newspaper every couple of weeks.
You can also go online and find several different ways to make winter stray cat shelters (cats are a similar size as opossums) out of old Igloo coolers, Styrofoam coolers or even Rubbermaid tubs. In making these structures, you want to make sure that any opening you cut is filed down or taped off so as not to cut an animal going in and out. The opening should not be more than 12” in diameter. If an opossum can get its head in, it can get the rest of its body in. Whatever structure you use, make sure it is weighted down or stable enough that an opossum’s busying around, rearranging all the nesting material you’ve placed inside doesn’t knock the structure over with the entrance face-down, trapping the opossum in the den box.
Having a den box in your yard can provide an excellent opportunity for your children to “go hunting” for wildlife. Provide them with headlamps and search your backyard after dark and see if they can locate wildlife in your foliage or atop the fence. Have them observe the wildlife from a respectable distance, without hampering or hindering the animal’s movements. You might wish to smooth the surface in front of the den box, or layer flour or baking soda at the entrance and rake until smooth. Examine the area in the morning for footprints disturbing the material in front of the den box. Take cell phone pictures of the footprints without disturbing a possible sleeping animal inside.