Most child care is during the day. But I've seem familys look for overnight nanny's on care.com before. I myself work during the day but maybe a couple times a year the family I work for will ask me to do an overnight.
So child cares are overnight
Is it possible for one of you to change the hours that you work?
I am an experienced nanny of over 10 years for multiple families. I would say it doesnt hurt to ask your sister in law first. As far as what you should offer her I think it depends what hours she'll be at your house for, you said you work nights is it all night or like 6pm-12pm? You could pay her hourly or a flat fee per night. Also should take into consideration what you can afford to pay and what going rate is for babysitters/nannies in your area. If she says she's not interested I would suggest you check out Care.com to help you find an overnight nanny possibly.