Get rid of standing water, keep it away. Induce the habitat for some dragonflies and bluejays, they luv mosquitoes.
Mosquitoes are not attracted to "bugzappers".
Lime is generally used for eventual deterioration of tree stumps. Takes more than one year for full removal. Will have to be reapplied on a regular basis. Not a smart thing to do in such close vicinity of children playing area.
Another way is to build a few fires on the stump. Has to be...