There are more words but they are from Tolkien's earlier conceptional periods. Tolkien likely changed these words as he evolved the aesthetics and completeness of the languages. You may even find languages that Tolkien later rejected. Do not mix words from different time periods unless you are familiar with the phonetic developments.
hen
noun. eye
uil
noun. hen
porogwil
noun. hen
The word G. porogwil appeared in the Gnomish Lexicon of the 1910s as a combination of G. porog “fowl (domestic)” and G. uil “hen” (GL/64, 74).
Neo-Sindarin: I would adapt this word as ᴺS. porochuil for purposes of Neo-Sindarin, updating the second element to the neologism ᴺS. huil “hen”. The longer form is better distinguished from ᴺS. huil “bitch, female dog”.
aigli
noun. bird
bil
noun. bird
A word for “bird” in the Gnomish Lexicon of the 1910s appearing next to G. bilinc “sparrow”, but this word was deleted and the gloss for bilinc was expanded to “a small bird, especially sparrow” (GL/22-23). The form bil appeared in a couple other places in the Gnomish Lexicon (GL/23, 31), but seems to represent a “root” rather than a word. Tolkien indicated bil was derived from ᴱ✶du̯il (GL/31), but the exact mechanism whereby du̯- became b- isn’t clear, but a similar change is seen in 1920s ᴱ✶du̯ag- > ᴱT. baga- “beat” and ᴱ✶tu̯ak- > ᴱQ. pak- “apply, attach” (PE14/66).
sitha
adjective. this
Below: Tolkien's Late Period (1950–1973). These are from Tolkien's late conceptual period — his most settled forms of the languages. Prefer these over the earlier ones above when composing new text.
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.