Here are a few ideas…
Eliminate the light source… foliage needs to grow. Thick black plastic and mulch over the stump, carpet etc … blocks the light source
Caustic Soda (Sodium Hydroxide) solution will kill out the tree stump. Caustic Soda should be available at any hardware/paint shop. Make a solution (1 part caustic soda + 2 parts water) and pour the solution over the tree stump. It may be necessary to apply the solution three-four times before the tree stump is completely removed.
Digging around to expose all the major roots and the stump, then using a chainsaw or axe to cut these roots can help in either case.
Just keep drilling holes. When there is nothing left to drill, the stumps will decay quickly.
Use Herbicides (Root killers) with Caution. Herbicides are sold at Garden Centers / Hardware Stores / Wal-mart etc. They also sell a ‘Store Brand’ which is cheaper, but basically the same.