Eulalia is a melodious name with a southern drawl, thanks to those lilting double 'l's.
A teenage martyr, Saint Eulalia was born in Spain and is a patron saint of Barcelona, where there is a cathedral in her name. One legend associated with Eulalia is that a dove flew out of her neck when she was killed, thus the association with both sweet speech and peace.
Eulalia is a character in William Faulkner's Absalom, Absalom; Marcia Gay Hardin has a daughter named Eulalia Grace.
Eula is the traditional short form, but Lalia or Lally would make more appealing and modern-sounding nicknames. The French version is Eulalie (subject of a Poe poem), in Spanish it's Olalla.