Elsie!
My friend has a daughter named [name_f]Elizabeth[/name_f] and everyone calls her [name_u]Izzy[/name_u].
So if [name_u]Izzy[/name_u] was to long of a nickname you could shorten it to Iz. I hope this helps.
I love [name_f]Eliza[/name_f] or [name_f]Ella[/name_f] as nicknames for [name_f]Elizabeth[/name_f]!
My name is [name_f]Elizabeth[/name_f] and my parents never wanted me to have a nickname, yet they gave me the most nickname-able name there is. [name_f]My[/name_f] friends usually call me [name_f]Lizzy[/name_f] but I still mostly go by my full name. Sometimes nicknames unexpectedly pop up, like my closer friends also call me [name_f]Wednesday[/name_f] (which is a long story).
Betsy
[name_f]Bess[/name_f]
[name_f]Eliza[/name_f]
[name_f]Libby[/name_f]
[name_f]Tibby[/name_f]
[name_u]Izzy[/name_u] (a little girl I used to babysit called me this)
[name_f]Lily[/name_f]
[name_f]Lilibet[/name_f] (apparently the [name_f]Queen[/name_f] of [name_f]England[/name_f] was called this as a little girl)
[name_f]Zella[/name_f]/Zellie
[name_f]Eliza[/name_f]-[name_u]Jo[/name_u], [name_f]Lily[/name_f]-[name_u]Jo[/name_u], [name_f]Betsy[/name_f]-[name_u]Jo[/name_u], etc
I like [name_f]Libby[/name_f], [name_f]Eliza[/name_f], [name_f]Lily[/name_f], and Lilybet for nicknames!
My favorite nicknames for [name_f]Elizabeth[/name_f] are [name_f]Bett[/name_f], [name_f]Liz[/name_f], and [name_f]Ellie[/name_f]!
I like [name_f]Lizzie[/name_f], [name_f]Beth[/name_f] or [name_f]Eliza[/name_f]
Other suggestions:
[name_f]Libby[/name_f]
[name_f]Elle[/name_f]
[name_f]Ellie[/name_f]
[name_m]Hi[/name_m] there.
Aw, I love [name_f]Bette[/name_f]. I agree that [name_f]Liz[/name_f] & [name_f]Lizzie[/name_f] are way not as interesting. [name_f]My[/name_f] other favorites are [name_f]Bess[/name_f] & [name_f]Tess[/name_f].
[name_f]Hope[/name_f] this helps. 
The only new suggestion I have is [name_f]Zibby[/name_f], which I think is cute.
sorry for any repeats! [name_f]My[/name_f] favourites are [name_f]Bessie[/name_f], [name_f]Betsy[/name_f], [name_f]Lizzie[/name_f], [name_f]Elsie[/name_f], [name_f]Lilibet[/name_f], [name_f]Lillie[/name_f], [name_f]Betty[/name_f] and [name_f]Elise[/name_f]