Thanks to a simple Terminal command, however, you can permanently prevent Dock bouncing by any application. In Terminal, enter these two commands:
$ defaults write com.apple.dock no-bouncing -bool TRUE
$ killall Dock
When the Dock restarts, you won't see any icon bouncing again, ever. An ideal solution would be a per-application setting, because there may be apps for which you want a bouncing Dock icon. Lacking that, though, I'll take the no bouncing solution. To reverse this, just repeat the command, replacing TRUE with FALSE, and then kill the Dock again.
For an easier method of implementing this feature, see this hint.

