As a devoted grandmother, I can sympathize with your problem.
However, I can't say I agree with your appraisal of the situation. I think you and the baby's parents have to get on the same side, not opposite sides, of the situation. At a relaxed time, when the baby is asleep, discuss the situation with the parents and indicate that you know how frustrating it must be for them to have their son cry and whine so much. (You can be sure that they have noticed that his cousin doesn't cry all the time—and they're probably worried about the inevitability of favoritism on your part.)
Center the discussion around why the baby cries and whines all the time, not their way of handling it. Bring up the possibility that there is a medical cause that has not been identified. Certainly teething could be a factor. Discuss strategies that have not been tried—like letting him cry it out occasionally, how long they should let him cry before intervening, and clever ways of distracting him, etc.
Finally, I have to take their side a bit. It has been found that children who are picked up and held when they cry during the first year of life (especially the first six months) cry less rather than more later on â€¦so stay tuned.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.