Hello Autumn, and welcome to planDisney!
Great news, you are able to pay for a
World of Color or a
Fantasmic! Dining Package with a
Disney Gift Card for certain dining packages. The
World of Color Dessert Party requires advance payment online or in the
Disneyland app, and requires a credit card to purchase. The
Fantasmic! Dining Packages require a credit card to hold the reservation, and then you should be able to pay in-person with your Disney Gift Card the day of the show.
My family has always loved the Dining Packages since you get to enjoy a fantastic meal as well as not stress about finding a great place to view the
nighttime spectaculars. Our favorite dining experience is
Blue Bayou Restaurant, you just cannot beat the ambiance and watching the Pirates of the Caribbean boats go by! If there is availability to sit near the water when you check-in, I highly recommend it!
I hope this information was helpful for you Autumn, and please do not hesitate to bring any other questions here to planDisney!
Have a magical day!
Melissa