how to kill the stumps

Fertilome makes a product called Brush & Stump Killer that has worked for me most of the time. Just make sure you apply it right after you cut it. You don't have to drill holes, but you do have to apply it (paint it on) to the xylem (outer ring, just inside the bark).

TO kill Schinus stumps
Either Roundup concentrate at full strength mixed with a bit of dish detergent or, if you can get it "Garlon' mixed 10:1 with water.
Both should be brushed onto the stump as soon as possible after cutting.
If you have the time and manpower, you can monitor the regrowth and knock off the epicormic shoots or chop'em with a machete. Eventually the stum starves and dies, I have done it but it can take a long time!

usually, the garlon or roundup has only to touch the cambium growing layer of the stump in order to kill it. so you can paint the cambium only with good effect. with eucalyptus species, however, the entire stump including the outside bark may need to be completely painted with herbicide material in order to thwart dormant/latent buds.