Refreshed the braincells.....
Epsom salts!!
High grade pure stuff - from a decent garden shop or nursery.
Cut the stump as close to the ground as you can.
Drill lots of holes in the stump - as deep as you can - extended length 3/4" or greater spade bit is good.
Skinny stumps are probably better with 1/2" holes.
Fill the holes to within about an inch from the top of the hole, plug with paraffin wax - or dribble candle wax into the holes to seal them.
Wrap the stump in a plastic bag, cover with dirt.
It does take a while, but the lack of sunlight combined with the Epsom salts will kill the tree stump and it's roots - without poisoning the surrounding ground.
Then, when you get bored - invite the crew around for a beers and bonfires party!