Most computer monitors won't sweep much slower than 31.5 kHz horizontal and 60 Hz vertical. You need to find a computer monitor that can sweep at TV rates: 15.75 kHz horizontal, and 50 Hz or 60 Hz vertical, depending on your video standard. If your monitor doesn't sweep at those rates, then your project is dead, because you said you don't want to use any fancy video standard converter.
If the monitor also has "sync on green" (many do), then you can probably feed your composite video signal straight into the green input, and you'll see a green TV picture. If that works, feed you signal into all three inputs (with suitable buffering) for a black&white TV picture, or build a chroma decoder (like in a TV set) to get full color.
Additional problem: some computer monitors resist interlacing, and will jitter vertically or misalign the two fields.