As a nitpick the proper term is "cryptocurrency", not "digital currency". A cryptocurrency does not necessarily have to be stored or generated digitally.
How would a non-digital cryptocurrency work? While signal scramblers, an analog equivalent to digital cryptography, did exist, I have a hard time imagining an analog blockchain.
It being digital is just its encoding. An analog cryptocurrency could be carved into trees or anything.
Just to be clear. I do agree with the argument above that "cryptocurrency" is a much more fitting term than "digital currency".
I suspect there are chemical compounds that when reacted can perform analog arithmetic. If you used that to create signing, hashing and propagation logic I dare say analog cryptocurrencies could exist.