Cut two pieces of 1-inch-thick plywood or other strong wood to measure 8 inches across and 8 inches wide. You can make the platforms a little bigger if your area tends to attract a lot of pigeons, but make sure they are the same size. Cut with a table saw.
Drill a small ½-inch-diameter hole ½-inch deep in each of the four corners of each platform. Make sure the holes line up with each other when the platforms are laid face to face.
Cut four dowel rods to measure 8 inches high. These rods will hold the top platform away from the bottom.
Coat the bottom and top ½ inch of each dowel rod in wood glue. Insert the bottom of each rod into one of the holes in the bottom platform and the top of the dowels into the corresponding holes in the top platform. This creates four columns that support the weight of the platforms. Allow the glue to dry fully before continuing.
Install your birdhouse at a height between 7 and 14 feet, or in the area where you keep finding pigeons. If you want to hang it from a ledge or tree branch, install an eye hook in the top with your drill and thread strong cord through the eyelet and around the ledge or branch. You can also set the house on a long pole or fence post; hold it in place with a few screws through the bottom or with strong wood glue.