The Square card readers that plugged into the headphone jacks were also analog modems. Well, the swipe variants were just "mo" (modulators) and the phones were the "dems" (demodulators). The first chip card reader, that plugged into the headphone jack, built a full bi-directional soft modem onto either end.

In theory you should be able to update the firmware on one of the chip card readers with one of these vinyl records and a 1/8" adapter.