The word G. uil “hen” appeared in the Gnomish Lexicon of the 1910s (GL/74), almost certainly a cognate of ᴱQ. oi “bird, hen” which Tolkien considered deriving from ᴱ√OHO² “cry” (QL/69). In Common Eldarin: Noun Structure from the early 1950s, Tolkien had the primitive word ✶kholjē “hen” derived from the root √KHOL “crow, cry aloud” (PE21/82), which may be a later iteration of this Gnomish uil “hen” word.

Neo-Sindarin: Based on the above, Gábor Lőrinczi proposed a neologism ᴺS. hŷl “hen” as recorded in the VinQuettaParma Wiki (VQP). However, my analysis of Sindarin phonology indicates that ᴺS. huil is the more likely result ✶kholjē: compare thuil and thuin plurals of thôn and thôl, and possibly also ruin < *runyā and fuir < *forya. For further details see the entry on how final [i] intruded into preceding syllable in Sindarin.

In any case, I recommend ᴺS. huil for “hen” in Neo-Sindarin, or its more elaborate form ᴺS. porochuil.