Even in Dutch they use the word konijn, I actually had no idea that "coney" was an English cognate for that word until reading this thread, I love learning these associations as making connections like this really helps in learning new languages.
I knew about Coney Island but I had never made the connection between Coney and Rabbit, I thought it was just a name.
Curiously there is another Isla Conejo / Rabbit Island near here too.
From Wikipedia:
It may be because when the Dutch people arrived in New Netherland, this island had many rabbits, so they named it 'Konijn Island', which became 'Coney Island', using the archaic term for rabbit in English.
You are; coney in English generally has a long e sound at the end (like saying the letter 'e'), not a long a sound (like saying the letter 'a'), so it wouldn't be the same or rhyme with the first two syllables of conejo (which has the long a sound in the second syllable).
Tangent, but in line with what others have commented, American English tends to pronounce the first syllable with a long o (like saying the letter 'o'), whereas British tends to pronounce it with a long oo sound (like the vowel sound in the the word 'food'). I've never heard it pronounced with a short 'u' sound (an 'uh' sound), but others intimated they either have, or have heard it pronounced close to it, which is interesting.
> conejo (which has the long a sound in the second syllable).
The Spanish word is pronounced more like "koh-neh-hoh" (or [ko'neho] in IPA), no "long a" ([ei] in IPA) there. The English "long vowels" (diphthongs really: a combination of two vowel sounds) would be written with two letters in Spanish (and IPA).
Good clarification. Depending on the variant of English, "long e", "long u" and "long a" may or may not sound like diphthongs. They can be analysed as /ij/ and /uw/. Wikipedia puts them under "potential diphthongs".
Edit: I may be assuming an incorrect pronunciation of coney. Even as a native speaker English sucks.