The American Grandparents Association lists trendy for grandmothers that include GG, Glammy, Kitty and Uma, and playful names such as DearMa, Mamabear, MaxiMa and Queen Bee. SFGate notes the trends of turning to the family's ethnic heritage for ideas or letting the grandchildren decide what name to use.
Some words for grandmother in other languages that may work as nicknames include the Spanish Abuelita and its derivative Lita; the Swahili Bibi or Nyanya; the informal German Oma; the Italian Nonna; and the Swedish, Danish and Norwegian MorMor.
Nicknames based on the grandmother's first name are another option. For example, the American Grandparents Association gives "Zannie" as the name grandmother and actress Suzanne Somers uses.