Jake,
On small diameter growth such as you have, a quart of Ortho Brush Killer and a $1 throw-away paint brush is a good method. I pour the brush killer in an old coffee can or similiar and paint the chemical on the cut stump and the sides of the stump, clear down to the soil level. Put a good, wet coat on the stump and you should not have any re-growth.
On larger diameter stumps, say 8" or greater, cut numerous grooves in the stump with your chain saw before applying the chemical.
