We'd gotten as far as Latin cotoneum/cydonium malum last time, and the development and spread of the Romance languages does some funky things.
With cotoneum (malum) we see the same phenomenon as the continuation of Latin (caseus) formaticus (cheese mold-made) where the adjectival element gets continued as the name itself (fromage, formaggio, etc.) There are exceptions, though: caseus remains in English "cheese", German "Käse", etc. The same sort of thing, in yet another aside (this one promised), is why our continuation of Greek melon "apple" now refers to fleshy Cucurbitae--originally melon.pepo(n) "apple-gourd" in Greek and Latin, with the original gourd element clipped off as unnecessary.
Anyway, cotoneum/cydonium is what we have to work with: respectively (1) and (2) from here on out.
Old French: cooin. From (1). The loss of final Latin -m is common to Romance languages, and contributed to the erosion of -VC case endings. The intervocalic deletion of /t/ is harder for me to account for, but seems to have happened anyway, resulting in two contacting vowels which became a diphthong. Later on in French the final nasal went velar, resulting in the current French coing. There is a place name Cotignac in France which alone seems to have kept the intervocal /t/, place names being hardier at this sort of thing, and the name also refers to a kind of quince preserve.
Before it turned into coing, Middle English borrowed the Old French word cooin, reshaping it as coyn or quyn, developing the initial labiovelar /kw/. Things start to look familiar. The Middle English plural of quyn was quynce, which was later re-evaluated as a singular, thus giving us the singular quince. Singular indeed, though not a singular occurrence in English. "children" and "brethren" are double plurals like "quinces," although alone much different lines. Both of these were originally r-plurals (cildra/cildru and brether) which got extra -en endings tacked on when they were no longer viewed as being plural. Etymology or no, "quinces" it's still the valid English plural, though it now strikes me as funny. English also has an archaic quiddany, (from (2)?), referring to something not quite a syrup and not quite a jelly, and cheerfully stole the French cotignac, leaving us with a bunch of Enlightenment-era cookery-book references to Cotiniack. Delightful.
We've gotten sidetracked from the Romance languages. Spanish has membrillo (epentetic b following metathesis!) and Portuguese has marmelo, but Catalan gives us codonyer. The vowels make it look like (1) with the intervocalic /t/ voiced to /d/. The ending is baffling, but fascinating all the same. Walloon has "poere de cwin," "quince pear," developed from the French. Italian has mela cotogna, keeping Latin malum. Romanian has gutui. The initial voicing there is something else. I have no knowledge of Romanian historical phonetics, so I'll leave it at that.
I'll wrap things up with Germanic and Slavic, and Greek tomorrow for completeness' sake (I at least want to get to that, if only to babble about Czech for a while) and a view outliers, like Finnish and Japanese. The title should at least make a bit more sense now!