If you have a lighter socket near the TV, if it's a newer TV that doesn't need too much power you could just power it with a small inverter that has a lighter plug on it. There is more impedance and hence voltage drop between the battery and the inverter that way than if connected more directly to the battery, but for a small load the total drop is small and it often isn't a real problem.
This, in fact, is exactly the setup I have. The only annoyance is the slightly noisy cooling fan in my inverter, and the fun of plugging and unplugging things to swap between shore power and inverter power. Having a quiet inverter would eliminate both problems as there's no real need to not use it when on shore power (the converter for the RV supplying more than enough to run the inverter and charge the batteries and operate the other 12V systems).
