Ah, so you have an audio channel that is being transmitted along with the video, and you want to send your NMEA data through that channel.
You can't just connect the serial data to the audio input because data needs to be DC coupled and the audio channel will not do that. The normal way is to use a modem, which converts the two possible states of the digital data line (0 and 1) into an audio signal. The simplest scheme is FSK, frequency shift keying, where a 0 is represented by a tone at one frequency and a 1 is represented by a tone at a different frequency, with a "dumb modem" IC at each end. The transmitter simply transmits the data as tones, and the receiver converts the tones into a digital signal.
The trouble is the data rate and bandwidth. 1200 bps was the maximum you could transmit using FSK over a telephone line with a bandwidth of around 3~4 kHz. If your data is at 4800 bps you'd need an audio bandwidth of 12~16 kHz, which I doubt your system would have, but in any case I don't think any 4800 bps FSK modems were ever made.
Other standards used on telephone lines achieved higher data rates but required extra trickery such as adaptive equalisation which requires a bidirectional communication path, and they used a lengthy negotiation phase too.
A company called CML makes modems that can handle higher data rates using FFSK and GMSK modulation schemes but I think these are all synchronous, so you couldn't send asynchronous serial data through them.
See whether you can change the NMEA data rate on your GPS device. You'll probably also have to disable various sections of the data otherwise the message will be too long for the once-per-second update rate.
Alternatively you could add a small microcontroller to receive the standard NMEA data at 4800 bps and retransmit it at a lower rate with some kind of customised format.
Either of these options would allow you to use a 1200 bps dumb modem at each end of the link. Some microcontrollers can be programmed to generate and receive modem audio directly, to avoid the external modem IC. Google some of these keywords and see if there is any clear solution available.
Also, post any technical information you have on your transceiver system, such as the bandwidth of the audio path.