There are many people who have problems tuning in modern TVs to the old computers.
What I have, and I recommend that you keep an eye out for on eBay (they do turn up now and again) is a Philips TV Tuner, model 7300. It was produced around the time of the Amiga, and was intended to display normal TV pictures on the Philips monitor.
This is a real analogue tuner, that takes in a normal TV signal and outputs composite video and also an audio signal onto two phono connectors, so you can plug it into the "AV" sockets on your TV, bypassing the troublesome digital tuning.
It comes in a cream coloured case (nicely retro!), and has 12 preset tuning channels, using old fashioned thumbwheel tuning (nothing digital).
I use it for most of the old computers and is great as you can fine-tune without the TV deciding that it's not going to lock on.
Anyway, hope it is of use

Regards.
Grant