Can you list a few polysyllabic words that only have one vowel (not including y, since it is viewed as a vowel in some words)?
I understood your question in a completely different way. If this is not the answer you were hoping for, I'm sorry, and I hope you enjoy these words anyway. This sentence contains seven polysyllabic words with only one vowel.
The men flee these entrenchments where legless men bleed.The severed members, strewn helter-skelter, redden the cerements.
This is a quotation from EUNOIA by Christian Bők; page 45. Every page sticks to one vowel for about a dozen lines. Now p.59
Old colophons on schoolbooks sport rococo scrolls on worn morocco.
A syllable is normally thought of as being a peak in sonority. Sonority can be understood as something like "musical loudness".
Vowels are considered to be more sonorous than consonants, because they are perceived as consisting of a pitch or note without any (or much) frication / turbulence. Pitch is that sense of a sound clearly having a high or low note. These sounds have periodic (regularly repeating) waveforms.
In English, the nasal consonants and the approximants /m, n, ŋ, l, r, w, j/ are thought to be the next most sonorant group of sounds. They also basically involve periodic wave forms, although there is some sort of obstruction meaning that the air doesn't leave absolutely freely through the mouth.
Next there are sounds with pitch and turbulence together. So these have waveforms which are a mixture of periodic and aperiodic waves. In other words you will see a regular, repeating pattern overlaid by random messy waves (or you can think of it the other way round if you'd like). The important thing is that you get both of those together. So you get a messy frictiony sound like air escaping from a pipe overlaid with a kind of musical note. Some examples are /v, z, ʒ/
Lastly, you get sounds that have no pitch at all. They just involve turbulence in the air. You can think of these sounds literally as air escaping through a hole in a pipe. (This is actually exactly what they are!) Some examples are /f, s, ʃ/.
Some syllables in English can be realised by an occurrence of one of the nasal consonants /m, n, ŋ/ (that last sound is the last sound in "sing") or the liquid approximants /l/ or /r/.
So, for example, the word bottle /bɒtl̩/ has two syllables. The first has the vowel /ɒ/. The second syllable often consists just of the sound /l/. It doesn't have a vowel. We still perceive this as being a syllable even though it doesn't have a vowel, because [l] is much more sonorant than [t]. So after the vowel /ɒ/ we have /t/, which isn't at all sonorant - and then we get an increasing sonorance with the /l/. There are therefore two peaks of sonorance in this type of pronunciation of the word bottle. So we perceive two syllables. But there is only one true vowel.
Polysyllabic words with (potentially) only one vowel
Here's a few words which are often pronounced with only one vowel. Once you spot the kind of pattern you'll be able to think of thousands of others:
It uses y as a vowel, but the y is the only vowel: "Rhythm" (two syllables).
I just thought of another one: "World" (two syllables). In as much as some sources say it's only one syllable, in most of America it's pronounced as two: WER-uld.
Why insist on even one? Why not go for zero:
crwth has both a monosyllabic and bisyllabic pronunciation. This cheats though by taking your question overly-literally and assuming your saying "not including y" means you are only excluding that letter and the letters that are typically vowels, namely a, e, i, o & u. In crwth the w is a vowel, used as w is used as a vowel in Welsh, from which crwth is a loan-word.
Likewise, tsktsk has no "vowel" letters and is bi-syllabic, but it does contain vowels in that it is pronounced /ˌtɪskˈtɪsk/.
To look at it the other way, if spoken in a rhotic dialect, and if you consider the [ɹ̩] of such dialects a syllabic consonant rather than a vowel, then burglar, turtle and many other words have no vowels.
From this beginning of zero we can easily have one:
crwth but acknowledging that w is a vowel.
burgled (though even this could perhaps be spoken with no vowels).
There must be some others, but these spring to mind immediately.
“ Fred is a two-syllable word. ”
That's a quote from the actor who voiced Wilma Flintstone,
quoting herself, almost two full paragraphs below the heading
‘ The Flintstones ’
To hear is to believe: