You'd have to do the power requirments for a TV, but my feeling is using an inverter to a deep cycle battery and then hoping a solar charger will replenish it isn't going to work.
I never had a TV on my old 22, but I did have a Stereo and VHF Radio. I bought a glass solar panel from Harbor Freight, a plastic cutting board from Home Depot and a stern rail clamp from West Marine. I cut a hole out of the middle of the cutting board for air flow, attached the solar panel to the board and attached the stern rail clamp to the bottom of the cutting board.
The clamp was the type used for grills, so I could loosen the handle and drop the panel down along side the stern rail. When I was gone, I lifted it up to soak in the sun. The second year I bought a regulator between the panel and the battery to stop reverse trickle.
This system worked very well for me. I had an electic start on my motor and I ran the stereo all the time while sailing. I used the boat from May through October and never had an issue with a dead battery.
I wish I had details on the panel and such, but I sold the boat...
I included some pics of the setup. I also had an inverter that I ran to an outlet, but I never used it.
Chris