How to romanize the word "mem, ayin,yud,yud,nun,yud"?

"Ma'ayene" is correct, per Even-Shoshan and all AACR2 records in the LC database.  The vowels are mem-patah, 'ayin-patah, yod-sheva, nun-tsere.  One might possibly consider romanizing it "ma'aine," but this solution is obviated by p. 17
of HCM, which prescribes that yod-with-sheva has to be transcribed "ye" if the yod is the 2nd consonant of a root.  (To be sure, the paragraph is talking about verb-forms, but LC takes the rule to apply here also.) Unfortunately the Hebrew romanization table doesn't allow "ma'ayne."  The sequence "ay" appears only if the yod has a vowel other than sheva
(as in, e.g., "bayit").