“…Similarly farthing has been used for the
four divisions of the Shire, because the Hobbit word tharni was
an old word for ‘quarter’ seldom used in ordinary language,
where the word for ‘quarter’ was tharantin ‘fourth part’. In
Gondor tharni was used for a silver coin, the fourth part of the
castar (in Noldorin the canath or fourth part of the mirian).(20)”The Peoples of Middle Earth, II. The Appendix on Languages, JRRT, ed. C.T.
This, aside from mentions of gold pieces and “silver pennies”, is the only passage I can find concerning currency in Middle Earth. Not much to work with, but suggestive of a long-reaching history nonetheless– like so many things Tolkien.
A few more tidbits (confirming the silver and gold currency as well as other stuff), relating to Elvish culture (possibly). From the erstwhile Darth Fingon’s excellent Linguistic Foolery series on the Silmarillion Writers’ Guild (Everyday Elves and What They Do):
Now that we have people to make all the things the Elves need in
their daily lives, we need to find somebody to sell the goods. Luckily,
the Qenya Lexicon provides words for pedlar (sic) and huckster. Just in case
you thought all Elves were honest traders. Other attested words
include barter, bargain, and words for silver and gold coins.Cf. the Qenya Lexicon, Parma Eldalamberon 12:
kulusta (n.) – gold coin
telpilin (n.) – silver coin
vaktelear (n.) – merchant
qapa- (v.) to swap or barter; to bargain
qapta (n.) good deal
Granted, these are derived from the earlier Qenya, but the evolution of the conlang gives us a modicum of insight into Tolkien’s thoughts on Elvish culture. IMO, for fannish purposes, one can run with it (and I have).
*clappity* MORE TIDBITS! TIDBITS FOR THE TIDBIT THRONE!
Every time I think I’ve successfully stripped the legendarium for parts, it turns out some giant swath of material has escaped my grasp! (…the existence of the Parma Eldalamberon confronts me with the terrifying question: how much money would I be willing to spend to have a table-top dictionary of obscure Quenya words? hmmmm…)
The coin words are particularly useful because it gives me a pattern to follow. I’d kludged together my own words for “gold coin”, “silver coin”, etc by just making the noun for the metals plural (i.e. “silvers”, “coppers”, etc.), and I was using “malta” for gold rather than “kulu”, the earlier form.
Excellent! TO THE REVISIONING! 
Thank you ever and again Prof Pandë, for pulling magical gifts out of your eldritch hat.
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