It seems there are some, but the examples are few and often obscure—at least if you're looking for words whose primary pronunciation in standard American English start with the ny- sound. (See yod-dropping.)
Searching the CMU Pronouncing Dictionary for words beginning with the N consonant followed by the Y semi-vowel returns the following results:
KNEW(1) N Y UW1
NEURAL(1) N Y UH1 R AH0 L
NEUROPATHY(2) N Y UH1 R OW0 P AE2 TH IY0
NEUROSCIENCE N Y UH1 R OW0 S AY2 AH0 N S
NEUROSCIENTIST N Y UH1 R OW0 S AY2 AH0 N T IH0 S T
NEUROSCIENTIST(1) N Y UH1 R OW0 S AY2 AH0 N IH0 S T
NEW(1) N Y UW1
NEWARK(1) N Y UW1 ER0 K
NEWARK'S N Y UW1 ER0 K S
NEWS(1) N Y UW1 Z
NEW_ORLEANS(1) N Y UW1 AO1 R L IY0 N Z
NUBIAN N Y UW1 B IY0 AH0 N
NUPENG N Y UW1 P EH0 NG
NUTE N Y UW1 T
NYET N Y EH1 T
Searching Moby Pronunciator for words starting with
n/j produces a larger set:
It's worth noting that these readily available and easily searchable pronunciation dictionaries are far from complete and likely contain errors. The CMU dictionary contains about 135,000 words, and the Moby dictionary contains about 175,000. In reality, more ny- words exist in English than are present in these dictionaries, and some words reported as ny- words in these dictionaries may not be legitimate ny- words.
Many of these results seem like false positives to me—either because they're not the sort of English words I'm looking for (e.g., acronyms, foreign place names, etc.) or because the words typically are not pronounced with the ny- sound in the English I'm used to. These are American dictionaries, though, and Merriam-Webster backs up some of the pronunciations but often lists the yod-dropped version first.
If you don't want to sort through the lists yourself, here are a few examples:
- words beginning with neuro-, e.g., neuropathy: Indeed, Merriam-Webster seems to list the ny- pronunciations as valid alternates.
- numerous, numerator, and related: Same concept as the neuro- words. I don't pronounce them that way personally, but apparently it does happen.
- nutant: drooping (apparently only in M-W's unabridged dictionary)
- nyala: an African antelope
- pneumatics: a branch of mechanics that deals with the mechanical properties of gases