You can still use the brine with some modifications. You should just make sure the bird is submerged in the brine.
The everyday brines call for 4 cups (2 quarts) of water. So just add an additional 2 quarts of water and that will give you 1 gallon of brine. If that's not enough to submerge your turkey, add the following: 1/2 cup sugar, 1/3 cup salt, and 3 more quarts of water. For larger birds add 1 cup sugar, 1 cup salt, and 1 gallon water. Then brine for 1 hour/pound.