I'm even a little put off by how pushy they are being about keeping your baby. You've said no twice already.
^This. I would be really worried about someone you didn't know asking you so many times. If it was your sister or something, you can expect them to ask over and over, but when it's a stranger I would be wary. Trust your instincts and find someone else.
Also, I'm a Nanny (well I used to be, I'm a SAHM now) and I would NEVER have behaved like this.