If you are going to train, commission for them only model is out of the question.
A nanny service is almost a commodity, there is only so much people are willing to pay, a lot of demand but not acquired by everyone. Your profit margins will most likely be small because essentially you are getting into a brokerage service for the nannies taking a commission off each placement.
Because of the low margins, you're better off maximum get each sale. Instead of making the primary business model based off 1 time hires/sales, focus on selling memberships... Try annual or bi-annual memberships that guarantees them a discount when they do actually hire, maybe offer faster or preferred services. This guarantees you operating cash flows month to month on top of the sales off each actual hire that pays for the nanny's hours worked and can give you an additional profit margin as brokerage commission.
Monthly + commission - (EBIT + Op. Exp)