How do I hire a caregiver for my sister who insists she is fine?

Your sister doesn't want change and may not want to admit she needs a caregiver. With you, she can just say this is my sister.

Since your sister has the money and you can't continue to be her only caregiver (very understandable) maybe you can try a little trickery.
You could hire a person to be your "friend" and visit you, then include your sister in this "friendship," gradually letting your sister learn to like and trust her.Then, you could move your friend into your sister's life more gradually without making it a big deal that this person is a "caregiver."

I do think you need to stand firm, no matter how you approach this, but if you can do it gently, it may be easier to get her to comply.

Good luck. Please check back and let us know how this is going.
Carol

Carol's idea is very good and very compassionate. I think it depends upon how advanced your sister's dementia is.

You can also take the ham-handed approach which is telling your sister that you can't and won't care for her 24/7 and that she is going to have to accept outside help or her living on your property will have to be discussed.

I don't think I'm as compassionate as Carol. :-) I think I've seen too many families held hostage by an elderly parent/sibling/friend who refuses outside help which forces the caregiver to assume the whole burden.

I agree with Carol's suggestion and Eyerishlass' caution. The longer someone becomes reliant on a relative, the harder it is to bring in someone else, and the more the caregiver suffers and feels trapped.

Pretending the paid caregiver is your friend and just concerned about your sister is a good way to open this avenue of care.