If it's cedar, it could take a while to rot on its own. Took one down for my parents and drilled a series of 1 inch holes in the top of the stump to collect water. A winter of freeze/thaw cycles busted it up enough to break up most of it. Not an ideal solution because the freezing would often only expand upward (like an ice cube tray). It was only one tree, and mom didn't want to get a stump grinder nor use chemicals. Couldn't burn in the city either.
Depending on height and diameter of stump, an angle grinder could work well on the smaller stuff.
