This method can work on any device, provided you are able to run modified code on the given device. In general this is the easiest approach on PC, provided GCII has no DRM or encrypted/packed EXEs which prevent this method.
If you are on PC, and your GCII executable has DRM or is compressed, you can try a hosts file workaround instead.
Note: Some other games will require opening another file, or multiple files, requiring you to perform the following steps for each given file. For example, some games might have a GameSpy.dll file, or Network.dll, or other files which contain the data which must be modified. These steps must be performed for each file where references to GameSpy exist. In the case of GCII's dedicated server, you must do the following to it as well if you want to run one on OpenSpy.
Step 1 - Open GCII's executable in a hex editor
Open gcii.exe with a hex editor, such as HxD.
Step 2 - Replace standard services
Replace all instances of gamespy.com with openspy.net
Make sure to not add extra bits - as that will break the GCII executable. If it says that it will, cancel and look at your search and replace command to see if it's not doing the above - even a space is a bit.
Step 3 - Save the edit
Don't worry, HxD will make a backup of the unedited version if you want to go back to it (or have made a mistake).
Step 4 - Make a GCII OpenSpy Account! (Ingame)
Once you've done this, you can start playing with people that has also made GCII use OpenSpy. Important: Make sure you have a backup way of remembering your password and nickname, just in case you forget.
Step 5 - Multiplayer?
Join our Ground Control Discord Server! It might be a bit GC focused for your liking, but you can change that.
The game times out trying to connect to anything
Yep, the only the thing you can do atm is complain to openspy to get them to fix it.