If you can make the emulator use directdraw to display the game, then fraps should be working. Also I highly doubt that any of the other softwares work where fraps doesn't because as far as I know they all use the same technique (hooking into the directdraw/direct3d rendering process, catching the image and writing it to the HDD).
I'd need to look it up but I am pretty sure that I recorded games running in dosbox using fraps.
True. I'm also trying to record games run by DOSBox. Some of old ones are, however, bought from GOG. Could you guide me how did you manage to start fraps running with those old titles? I tried to run Postal and record, but each time after the game start, all I got was a black screen. Fraps configuration should be fine, since it's the same one I used to use about 1,5 year ago, when I was capturing motion screen from games like Crysis 3 and Dead Space 3. However, as I said above, it does not work for old games. Due to that issue I was rather thinking about some software, that would have a possibility to simply record the whole screen actions.
Ok for dosbox emulated games from GoG.com:
Go to start menu -> GOG.com -> "your game" and start "Graphic Mode Setup". In the "Basic Settings" Tab change the "Graphic Mode" to "Direct3D" that should enable fraps to capture the game's screen.
As for Postal I am not quite sure, but isn't that a Win 95 or Win 98 Game originally? Have you tried using compatibility modes? If the blackscreen only appears with Fraps running try disabling the Fraps FPS Overlay. In some older games overlays often cause issues.