Most modern VHF/UHF FM mobile rigs designed for Amateur Radio use have a "data" connector on the back. Currently manufactured dual-band examples include Yaesu FT-7900, Kenwood TM-V71, Icom IC-208H - they all have the same 6-pin mini-DIN "data" connector using the same main pinout.
The 6-pin data connector is originally designed for attaching packet radio TNCs and other data equipment, and usually has at least the following pins:
- TX audio in (transmitted audio)
- PTT (ground to transmit)
- RX audio out, "1200 bit/s" "normal audio"
- RX audio out, "9600 bit/s" discriminator output
I quoted the bit rates, since the radio documentation often cites these standard packet radio speeds, although in reality it's just audio, and the radio doesn't really care about any bit rates as such. The "9600" pin audio output is taken before audio filter/amplifier stages of the radio, and has a flatter audio frequency response that is good for high speed data such as 9600 bit/s packet or AIS reception.
Technically, you can run SSTV or PSK31 over FM, and that "data" connector will suit that purpose perfectly. But it's not overly popular in most areas, so you might have to talk some friends to play with it. Most of SSTV and PSK31 activity is on HF SSB, although VHF/UHF digital chat as such should be a lot of fun.
PSK31 over FM in particular is quite strange and unusual, since PSK31 is designed to be a very narrow-bandwidth (31.25 Hz) mode for SSB transceivers, and transmitting it over FM (some 20 KHz) would be a waste of perfectly good radio spectrum and transmitter power. It works, but it's not efficient. Then again, it might be fun, and if you live in an area where most of 70cm is almost completely quiet and inactive (like I do), a little inefficiency on an irregular basis is not going to do harm, if you're having fun. A lot of amateur FM voice communications don't have a lot of useful information content, either.
SSTV isn't so narrow (about 3 kHz), and there have been more or less official FM channel allocations for it. Some US web sites cite VHF/UHF SSTV AFSK FM calling frequencies. IARU Region 1 (Europe) SSTV(FM/AFSK) frequency for 70 cm is currently 433.400.
I also often use the "data" connector of my FT-7800 for recording received voice communications on a computer. Works fine.