I use both phrases regularly, but then again, I work from home and have the TV on 24/7. I leave the TV on when I sleep, and TiVo those programs that I think I'll have time to watch sometime during the day. But a lot of those end up being TiNos. And yes, when discussing television, a lot of folks (including me) use TiVo and TiNo as verbs.
TiVo is pronounced TEE-voh
TiNo is pronounced TEE-noh