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I'd go with a pretty much direct translation.

不死鳥の目
Fushichou no me (pronunciation of 'me' is as in Parliament)

I'm a bit confused with your kanji, the one you've used for eye isn't really the common one, 目 is far more widely used.
Also, just putting the kanji for immortal and eye together doesn't really work grammatically, fushi (不死) would become a 'na adjective', becoming 'fushiname' (不死な目) just sounds more logical.

There are various other ways of writing Phoenix in Japanese, ootori (鵬) for example, but the kanji looks a bit complicated (really only three radicals) and it just sounds funny (ootori - lit meaning, big bird)
不死鳥 sounds the best bet for the word phoenix as 'immortal bird' sounds a bit better, and a surprising amount of people that don't really know Japanese recognise 死 (death)