This doesn't answer the question regarding circuit implementation, but the Wikipedia articles on NTSC and Broadcast televistion systems have some relevant background, at least for NTSC used in the US. It's possible that PAL differed or that there were variations to NTSC for other countries, so if one of those is your primary interest please update your question to clarify.
The RF signal coming out of the computer is the same as would be used to broadcast from a station antenna, only much much weaker. Or better to say: the computer's output signal is like what the television would receive from a nearby television station if it were broadcasting on Channel 3 or Channel 4.
The audio signal modulates the frequency of a separate carrier near the video channel. In other words, the circuit would be that of an FM transmitter for a frequency offset from the channel 3/4 video frequency. Specifically, the audio broadcast for Channel 3 is
61.25 MHz + 4.5 MHz = 65.75 MHz and for Channel 4 the FM signal is at 71.75 MHz (up 4.5 MHz from the 67.25 MHz AM video carrier).
These frequencies are within the VHF radio band. Any FM transmitter circuit for VHF or higher frequencies should be ± suitable, and may be more in scope for the Electronics or Amateur Radio SE sites. See e.g. https://ham.stackexchange.com/questions/3639/simple-fm-low-power-uhf-transmitter-circuit and https://electronics.stackexchange.com/questions/408644/need-help-understanding-simple-fm-transmitter.
There may have been a fairly standard implementation used across home computers but I'll leave that to other posters if so. There are a number of pictures of RF modulator circuits on that article I found via a page on the Sup'R'Mod modulator.