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√OHO “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 VQP (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 [[s|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.
The word G. huil “bitch” appeared in the Gnomish Lexicon of the 1910s as a female variant of G. hû “dog” (GL/49).
Neo-Sindarin: I would adapt this word as huil “bitch, ✱female dog” for purposes of Neo-Sindarin as a derivative of later root ᴹ√KHUG “bark, bay” (Ety/KHUGAN), perhaps derived from primitive ✱khūgil; compare to S. huan “hound”.