The phrase "as a second gift" is correct and usable in written English.
It can be used when referring to an additional gift being given after an initial one.
Example: "I decided to surprise her with a beautiful necklace as a second gift for her birthday."
Alternatives: "as an additional gift" or "as a follow-up gift".
As a fortieth birthday gift to herself, Susan decided to be a raw foodist for as long as possible.
A more modern guideline suggests crystal or glass items as a third anniversary gift.
"David," Ebersol said, as he gave Stern a second gag gift, "you'll need this when you're trying to get the conference finals in the Town Car on the way home from the office".
He has been surfing since 1964 and insists he was the only youngster in Buffalo to get a surfboard as an eighth-grade graduation gift the following year.
As an eighth-grade graduation gift, Oracle founder Larry J. Ellison gave his son a purple acrobatic airplane.
It included events heavy in symbolism -- from a candle burning in the pope's window in a silent vigil for world peace to homeless men presenting sleeping bags as the first gift for the Christ child in the Vatican's life-size Nativity scene.
This would link it to "Iolanta," because in the lovers' climactic duet, Vaudémont hails light as the first gift of the creator.
And that we might live no longer for ourselves but for him, he sent the Holy Spirit from you, Father, as his first gift to those who believe, to complete his work on earth and bring us the fullness of grace.
"He sends signals to throw her off-balance, such as his first gift of the collector's edition of Tess of the d'Urbervilles.
She's the sassy gal who makes up for what she thinks of as a second-rate singing voice with a gift for snappy comedy at the microphone, enduring the sour testosterone on the tour bus, with Elvis Presley and Jerry Lee Lewis.
