I would guess you'd be messing with a circuit board inside the cabinet and that any TV lacking such a jack probably is old enough or inexpensive enough not to bother. Is there a headphone jack you could use?

You would need a schematic of the sound card or portion of the TV to even attempt to install an Audio Out jack. You could consider installing a Headphone jack, like steve o suggested. A jack could be wired from the speaker wires in that the speakers would cut out when you plug in headphones. Or if you have a Stereo sound on the TV, connect a Stereo Headphone jack from each speaker for that affect. What did you have in mind for this Audio Output Jack?

I want to install the transmitter for wireless headphones.