The word ᴱQ. haruni “grandmother” appeared in both the Qenya Lexicon and Poetic and Mythological Words of Eldarissa of the 1910s (QL/39; PME/39). It is a combination of ᴱQ. haru “grandfather” with the female suffix -ni. As there are no other alternatives, I would retain ᴺQ. haruni “grandmother” for purposes of Neo-Quenya.
Quenya
haruni
noun. grandmother
A noun appearing as mam “grandmother, mother” in the Gnomish Lexicon, derived from ᴱ√maƀ or mam “something nice” (GL/57).
Neo-Sindarin: As we have no other attested alternatives, I would use ᴺS. mam for “grandmother” in Neo-Sindarin, based on a Neo-Root ᴺ√MAB (from primitive ✱mamba), but would not use it as “mother” for which we have plenty of later words.