I don't know about TIVO, but the directv should work fine. I've had directv for a number of years and have never had a phone line hooked up to it.

If the TIVO is a separate unit, it's going to need a phone line to get the programming schedule. There might be a way around it, though, using your computer.
Check out the TIVO forum and see what they have to say.

Here is a link that might be useful: TIVO Forum

my Directivo unit has to dial up and get updates periodically. if i leave the phone line disconencted form it, about every 2 weeks it loses the programming guide.

you have a couple options though. if you have high speed internet sign up with vonage or someone else for VOIP. if not you can get a cradle for your cell phone that you plug into your phone jack at home. this allows you to use any standard phoen inthe house to talk via the cell. plug your cell in at night, and then RX units will dial out over it to call in.