Hey there,
Unfortunately there doesn't seem to be a gift card option for the family terms. We are sending a gift code, which I am not sure can be used as a balance to pay off the family subscription of if it strictly is for 1 year of individual premium.
I'll try to contact Spotify and answer this though.
*UPDATE*:
Gift cards cannot be used for Family Subscriptions. Official Response from Spotify:
"It currently isn't possible to use gift cards on Premium for Family subscriptions. We also don't have any news about a gift card for the Premium for Family subscription, but we'll make sure to let the right team know it's something you'd like to see. Give us a shout if you have other questions."
Thanks!