Live-in nanny could work for sure, each nanny has there own ideas on how flexible they like to be. Au-pair could work (although they aren't supposed to work more than 30 hours a week, so not sure how many hours you would usually need).
Try Parental Choice, they are an agency specialised in finding flexible care.
Or, if you prefer advertising yourself, mention 'should be willing to accept working hours around varying work shifts' and mention average hours per week you would need them. Of course you would pay extra for flexibility.
It can work well to offer to pay a set number of hours per week for instance, even though you sometimes don't use all those hours (as your husband is covering most of the late and nights shifts that week).
But it all depends on the person. There are lots of people, with lots of different wishes. There may well be one out there who loves the freedom of working varied hours!