Middle Primitive Elvish
neinē
noun. tear
ney
root. tear
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.
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.
Tolkien used similar forms throughout his life for Elvish words connected to “tears”, the most enduring being Q. Nienna “Lady of Pity and Mourning” and S. nirnaeth as in Nirnaeth Arnoediad “[Battle of] Tears Unnumbered”. The first manifestation of this root was as ᴱ√NYE(NE) “bleat” and ᴱ√NYEHE “weep” in the Qenya Lexicon of the 1910s, though Tolkien considered moving all the derivatives of ᴱ√NYE(NE) to ᴱ√NYEHE (QL/68). Nonetheless it seems the distinction survived in the contemporaneous Gnomish Lexicon which had both nı̯e and nı̯eχe as primitive forms (GL/59-60). Early derivatives include ᴱQ. nyé “bleat” and ᴱQ. nyéni “she-goat” along with ᴱQ. nyére/G. nîr “grief” and ᴱQ. nie/G. nîn “tear”, the last of these appearing in G. Nínin-Udathriol, the earliest name of S. Nirnaeth Arnoediad.
The root reappeared in The Etymologies of the 1930s as ᴹ√NEI̯ “tear” (Ety/NEI), though Tolkien considered and rejected alternate roots ᴹ√NEÑ (EtyAC/NEI) and ᴹ√NEI̯(ET) “moist” (NEI̯(ET)), the latter becoming the primitive word ᴹ✶neiti > ᴹQ. níte “moist, dewy” and N. nîd “damp, wet; tearful”. Other derivatives include ᴹQ. nie “tear”/N. nîn “tear” (same as the forms from the 1910s) as well as N. nírnaeth “lamentation” (Ety/NEI). Tolkien’s continued use of Q. Nienna (S/28) and S. nirnaeth (S/192) in later versions of the Silmarillion indicate this root’s ongoing validity.
Neo-Eldarin: For purposes of Neo-Eldarin, I think some of the Quenya nye- forms from the 1910s might be salvaged as abnormal vocalization from n(e)ye- < √NEY.