。
She's been hoping for a present nonstop.
Literal
She [topic-は] present [object-を] persistently is-hoping-for.
しきりに ('frequently, persistently, eagerly') is a mimetic-flavored adverb for repeated, eager action — saying it over and over, or thinking it again and again. 望む ('to hope for, desire') in ~ている form marks the desire as ongoing. The pairing creates a picture of someone who keeps angling for or hinting about a gift — a vivid, slightly comic insistence.