This is the issue for me. Regardless of what he’s saying, why is he saying things to you that he knows upset you? Is he just trying to be funny? Or is he pissed at you for some reason?
My only advice is to sit down with him some time when the comments are not being made, and asking to have a serious talk with him. If you could explain to him that those types of comments really upset you, and hurt you, and you’re not just pretending to be upset, maybe he’d agree to stop. You could ask him: You know how much I hate this; why do you do it? Because if you’re doing it because you’re mad at me, please tell me what’s wrong and we’ll work it out. But if you’re doing it just to get a rise out of me, it really, really hurts my feelings. Either way, I’m asking you to stop, as a favor to me, because I find this deeply offensive. I would also tell my other relatives, this has been really bothering me, and I’ve asked Bro to stop, because I find it so upsetting.
Then, if he continues, you know he’s not just doing the garden-variety “bug your sibling,” he is intentionally causing you pain and disrespecting you. At that point, I would start leaving the room each and every time he says it; not making a big deal about it, and not saying anything, just leaving. Even if it’s getting up from the table at Thanksgiving, just get up and go. If he still won’t stop, you have a bigger problem, IMO, than him using the “N” word, which is that he is disregarding your very strong feelings. You’d have to decide how badly you want to spend time with a person who cares so little about you that he intentionally offends you. If it were me, I probably would tell him, you use this language even though I’ve specifically asked you not to; it’s not fun for me to see you anymore. I go home upset and crying because you care too little about me to respect this one request. I’d rather just not see you and remember all the good things, than have our relationship poisoned by knowing that I don’t mean enough to you for you to stop this. And then I wouldn’t see him anymore. I’d make arrangements to see other family separately. And I’d have the exact same conversation with every family member who used that sort of language: Please stop. I’m serious. I really hate this. I’m not kidding. I really really hate it, and I don’t understand why you won’t stop when you know it is very important to me. If you don’t stop, I won’t be able to see you anymore.
I wouldn’t get into any argument about who the term applies to, or free speech, or whatever, because that’s not the issue. Yes, you are free to use whatever hateful offensive speech you choose, but I expect you not to use that language around me because I’m your sister and it makes me sick to hear it and I’ve asked you not to say it. It’s not about language; it’s about respect.