Are you playing GOG.com edition or the original game on DOSbox you have installed yourself, or some other method? Also, do you have a very old computer?
From my experience the GOG.com version seems to run well on any modern computer. However I've had those slowdown problems with custom DOSbox installations (adjustable by changing emulation speed & other settings) and with very old computers (I've played the game on a 486 33 MHz, that was quite sluggish).

I had the same problem, the game itself ran good even when limiting dosbox to 10% of CPU, but the moment you moved mouse around it started stuterring and flickering. Setting "output=surface" instead of "overlay" in
dosboxSettlers2.conf fixed the problem and now it runs smoothly.

The easiest way to get rid of all kinds of stuttering with DOSBox is to change the output into opengl instead of overlay or surface, assuming your computer supports opengl properly.

Thanks for your advice, that helped. I tried first with opengl, but it was worse than with overlay. Changing the output to surface fixed the problem with my computer (Celeron 540, SiS Mirage 3).
dosboxSettlers2.conf (in Settlers 2 GOLD folder)
...
windowresolution=original
output=surface
autolock=true
...