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.