I think it would break the sonority principle, but. Who knows...
I was thinking on a similar thing to semivowels, it seems they are only possible between vowels, if there is one between two consonants, it's not a semivowel, its a vowel, but I don't know.
It is quite rare, but it arguably exists. Fante Akan has syllabic consonants which appear at ends pf words, preceded by a vowel. Such a word can be followed by a vowel-initial word, thus [ɔ̀pám̀ àtàŕ] "he sewed + a dress" (accents are tone). The historical explanation is that final CV was reduced to a syllabic consonant in some contexts, so compare Akuapem Akan [àtàdé] "dress". A similar example is Logoori, where the locative clitic /mʊ̀/ optionally reduces to [m̀], so you can get [kʊ̀rɪ̀ɪ̀ndà m̀ áváànà] "to-watch+in-there+childen". Finally, in Swahili, the class 1 object prefix on verbs is [m̩]. Most verb roots which begin with vowels do not eliminate vowel hiatus (though a few do, in some contexts), giving rise to forms like [wa-me-m̩-ondok-e-a] "they went away for him" (morpheme boundaries added).
As far as I know, there are no cases of underlyingly syllabic consonants between vowels within a morpheme – such things always seem to arise by rule, of some sort.
The Japanese letter ん represents a moraic /n̩/ sound, which always follows a vowel. Finally, it sounds like [ɴ], the uvular nasal, but elsewhere, its pronunciation assimilates to the following consonant's place of articulation. Wikipedia's article about the letter states that it "is followed by an apostrophe in some systems of transliteration whenever it precedes a vowel", in which case it is realized usually like [ũ͍] or sometimes [ĩ].
That article gives no examples of words containing n'. But off the top of my head, I remembered the name of the failed Shin'en space probe, which is four morae /si-n̩-e-n̩/. A bit more digging turned up the boy's name けんいち (Ken'ichi), consisting of four morae /ke-n̩-i-ti/. Draconis pointed out another in a comment: 恋愛 (れんあい, ren'ai), meaning "romantic love", is also four morae /re-n̩-a-i/. In each case, /n̩/ is a full mora but may belong to the previous full syllable depending on how your linguistics professor defines a syllable.
See also the Japanese Language Stack Exchange question Difference between んい (n'i) and に (ni).