Using 30" cinema display as TV I have the old (now discontinued) 30" cinema display, but I don't use it that much anymore so I'm thinking of converting it to a TV if possible.

Yes I could get a TV tuner but I'm not sure about the cables, how would it connect with TV tuners? I already have Mini-DisplayPort to Dual-Link DVI cable, is there any TV tuner available that supports it?
I've never heard of a DisplayPort-based external TV tuner.

But there are HDMI-based TV tuners available, and HDMI-DVI adapters are cheap.

Single-link DVI supports 1920x1200 at 60 Hz, which is higher than any digital broadcast TV standard, so that wouldn't be your limiting factor.