How can I get paid to assist my sister in the care of her husband?

As said, he needs to be on "in home" Medicaid to get any help there. Some states don't pay family. PA has a program where you train thru an agency, they hire u and they allow u to care for a friend or a LO.

Contact ur Social Services and see what programs are provided.

Depending on the State you reside in, must have Medicaid or Medi-Cal insurance there are State Programs that can assist. If do not have Medicaid, must apply at your local Social Service Office. The National site for locating local State Social Service Agencies. https://www.usa.gov/state-social-services If she is a Veteran or spouse of one- Look into the Aide and Attendance program at va.gov

If your BIL is a Veteran it is possible that the VA will pay his wife or you to care for him.
If he is a Veteran contact your local Veterans Assistance Commission they can help determine if he qualifies for any program the VA has. It might be a little or a LOT of help.
Contact local Area Agency on Aging or the local Senior Center they may be aware of programs that he may qualify for.
And lastly your sister can pay you to care for him. Make sure this is "legal" and documented as later on if proof needs to be shown that money was "given" it was for his care not a "gift"

Is your sister on Medicaid (Medi-Cal in CA)? The IHHS program can pay a caregiver if the care recipient qualifies for care. Apparently the pay tends to be low and the hours paid for limited.

The sister has to pay you directly. Or you get employed with an agency that she pays.