The church gives the NYI a check for a set amount of money each month, which they spend as they see fit.  They have their own bank account that I do not keep track of.  How do I record this in NTS?

Only one expense account will be needed to track the money given to a department such as NYI. The one account will track how much money is given to them but not how or when the money is actually spent by the department.

When writing a check to the department, use the one expense account for the entire department. See the example below.
Example Check