I would suggest Liz, Lizzie, Beth, but my favorite is definitely Libby.
i would suggest Liz Lizzie Beth too but maybe just eliza (e-lie-za) that's how to pronounce it.
Ellie, Ella, Lizzie
Her Majesty Queen Elizabeth does not have nicknames.
Good Queen Bess and the Virgin Queen are two amongst many.
Good Queen Bess, Gloriana, The Virgin Queen
Elizabeth Imus goes by Elizabeth Imus-Zero, and Elizabeth Zero.
Elizabeth Coyle goes by Liza.
Elizabeth Schell goes by Lizzie.
Elizabeth Spaetzel goes by Liz.
Elizabeth Sampson goes by Sam.
Elizabeth Sepulveda goes by Beth.
Elizabeth Vellozzi goes by Lizzie.
Elizabeth Reiners goes by Beth.