While I tend to use Fraps on almost all of my Steam games, I've notice that its not quite compatible with the games on here that use DosBox to run. Screencast works pretty well, but I wanted to see if the good people of the community had any more suggestions as to a good capture program/device for the older GOG games. Any suggestions would be a great help.

DOSBOX has its own, built-in record feature. I suggest you to just use that, it works perfectly fine.

Aside from using Fraps, you can also make use of other game recording programs such as Bandicam, OBS, and many more. You can learn more about that in this post and check whether it’s what you want.
http://www.apowersoft.com/free-game-recording-software.html