It is fairly easy to do it yourself, particularly for a second job (because the tax code she will probably have has a simpler calculation).
The online HMRC service does not provide a payslip (or do SSP or anything more than calculate the tax for the week/month), but if you are organised with keeping records it will do the job.
I am an accountant and I used do do my own nanny payroll, but that was because I didn't want to pay the £270 a year that nannytax charge. That was before the other providers such as payefornannies became established, and I think that their service at £115 a year is well worth it for the time it will save you, the help you will get with SSP, year end and other matters.
If you want something even cheaper, for a simple payroll service (rather than a PAYE agent who will deal with HMRC for you) look at www.mypaye.co.uk which will cost you just £12 a year. No hand-holding, but SSP calcs, all record keeping, year-end and more done for you.
Finally, as Nick says, her other job is her business. If she earns less than £6,475 a year in that job she may want to get her tax code split otherwise she will have to wait till the end of the year for a refund (which will be 20% of the difference between what she earns and £6,475 so may not be much). If this is the case, a decent payroll agent will give her a draft letter to send to HMRC to arrange this.