The incentives that should be offered to bring users to a game I believe should be valuable and unique to the referral system only.
That way, users will be more inclined to refer users to the game. I've seen some pet sites use cash app rewards, like Marapets and Subeta does. So, everytime their referred friend purchase an Account upgrade item or cash app upgrade, they too, are always rewarded with credit.
I also like the idea of referral prizes that is in the form of trophies.
But, I'd think points and unique items are the best approach for starting a new referral system off, however, I like the idea of unlockable pets as well, but I like the concept of offering rewarding users with paintbrushes, or items that will be able to unlock those pets for them,
Such as, a golden item? A paintbrush? A map? If a pet site also has the option for customization pets, then items that give them special items that are only able via the referral system would be great as well.
Or, sunglasses? New pets? New armor? Nice hats? Suits? Shoes? Extra Wardprobe space? That only can be won and obtained via the referral system.