That's a few but simple things to fix. Its mostly your video connection and not obtaining a proper ground.
1) Replace your video cable with a short (3ft or less) RCA to RCA Video Cable. Some people use RCA to RCA Speaker cables and think that it will work and for the most part they do but the longer the wire the more susceptible it will be to picking up stray magnetic noise which will show up on the monitor. Also, the speaker wire is not ground shielded properly like a video cable.
2) clean the RCA Video ports on both the Apple IIc and the Monitor. A very fine Emory Cloth would be best, wrap it around the outside the jack and twist it a few times around to remove the oxidation on both ports.
3) move the Apple IIc's Power Pac away from the system as far as you can place it. It produced a lot of magnetic noise that a monitor and video cable can pick up.
These three alone should fix most video problems with the Apple IIc.
1) Replace your video cable with a short (3ft or less) RCA to RCA Video Cable. Some people use RCA to RCA Speaker cables and think that it will work and for the most part they do but the longer the wire the more susceptible it will be to picking up stray magnetic noise which will show up on the monitor. Also, the speaker wire is not ground shielded properly like a video cable.
2) clean the RCA Video ports on both the Apple IIc and the Monitor. A very fine Emory Cloth would be best, wrap it around the outside the jack and twist it a few times around to remove the oxidation on both ports.
3) move the Apple IIc's Power Pac away from the system as far as you can place it. It produced a lot of magnetic noise that a monitor and video cable can pick up.
These three alone should fix most video problems with the Apple IIc.