Qenya
atwa
conjunction. double; either/or, either/or; double
atwa e·karne atwa ela
either he did or he did not
matwa e·antane sine nyén atwa tyén
did he give this to mé or to yóu?
tanta
adjective. double
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.
This word appeared in The Etymologies of the 1930s with the gloss “double” under the root ᴹ√AT(AT) “again, back” (Ety/AT(AT)). It also appeared with this gloss in notes on The Feanorian Alphabet from the 1930s and 40s (PE22/23, 52). However, in Demonstrative, Relative, and Correlative Stems (DRC) from 1948, Tolkien said it was used for “either ... or” (PE23/107) as in atwa carne atwa luine “either red or blue”. It could also be used by itself to mean “or” as in á anta nin macil atwa ehte “give me a sword or a spear”. In DRC, atwa served as the basis for a variety of similar words such as matwa “which (of two)” or enatwa “the second (of two)”.
Neo-Quenya: For purposes of Neo-Quenya, I would mostly use atwa in the sense “either ... or”. For simple “or” I would prefer hya from the 1960s. For “double” I would use atatya, also from the 1960s.