I suspect it happens more than most families would like to admit, a grandparent plays favorites among the grandchildren. I remember favoritism within my family and how it hurt. Once my own grandmother described the reason she wouldn't be visiting my uncle and his family one Christmas: she said, "What's the point? E (my cousin) won't be there." Ouch. Then she added, "She's my favorite, you know." Double-ouch.
As a small child, I didn't understand why my grandmother talked about my cousin so much, so comparatively, and so glowingly. I liked her, too - still do! - but I remember thinking, "Hey! I'm right here in front of you and I can do some pretty cool things, too!" It was a competition I was destined to lose, however. E was my grandmother's favorite grandchild, no two ways about it.
Let me be clear that this isn't about a grandparent and grandchild having a close, special relationship. It's different than that. It when the the grandparent voices preferences and acts to the exclusion of the other grandchildren. It's blatant and overt - and it can be very hurtful. It's often the kind of thing no one looks for, but it still slaps you in the face.
At the core of it, grandparent favoritism isn't at all about the grandchild, it's about the grandparent. But for a (non-favorite)child to recognize, understand and internalize that - and not throw blame at the favored grandchild - is something entirely different. That's where we parents come in. First the parent needs to recognize and understand the behavior. That in itself can be difficult! No one wants to see poor behavior, especially among family members. It can seem so much easier to ignore it.
Once a parent is willing and able to see the favoritism, the parent can validate and reassure the child. A simple, "I see how hurt you are when Gramps says those things and does those things for your cousin," can go a long way to understanding. From there, a coping strategy - if not a solution - can be addressed.
Talking and coping
Sometimes it might be appropriate to address the favoritism with the grandparent. Sometimes it won't be. The ability to have a conversation about the actions and resulting feelings depends entirely on your family's dynamic. If you think you can talk productively to the grandparent, and do so gently and calmly, conveying feelings and possible solutions without accusing too much, then give it a try. Remember to treat the grandparent with respect, as you would want to be treated (and that can be hard when you or your child is feeling is hurt). Perhaps the grandparent could agree just not to voice the preference when around other grandchildren or in family groups. In this way, the grandparent is not asked to change their feelings, just recognize the feelings of others.
Some things don't change
Sometimes, no matter what you do, the situation doesn't change. Some grandparents are unapologetic about their preferences, and refuse to make any adjustments. That's tough. Even if you can't have a conversation with the grandparent with the situation, or the grandparent isn't open to different actions, you can come up with some coping strategies with your child - not to mention reassure, reassure, reassure. You could make sure that time spent with the grandparent is rather active so there is little or no time to let the favoritism issue rise to the surface. If your child handles a tough visit well, recognize that - and reassure, reassure, reassure.
In my own family, we never handled the situation with my grandmother very well. That's too bad, but it has also come to some good. My siblings and I still are very sensitive to the issue of favoritism, and are careful with our children and nieces and nephews to treat each of them as special individuals, with no one of the singled out for preferential treatment. I'd say, rather, we each have one special thing with each niece and nephew and we are developing stronger relationships all around. This is good for the kids, the grown ups and the overall family dynamic.