I'm a nanny myself (mostly infants and toddlers) who lives in JP and works part time. Obviously a daycare is MUCH cheaper than
a nanny. If I were a JP parent I'd join 'JP Moms" (I know, not fair!) as they are all connected togeather and know what is out there...or ask parents around if they live in JP they likely are members if one is a mom!
A really good agency is Parents-In-A-Pinch (google them, they have a good website)...they place longterm nannies but also have
reference-and-background checked nannies to help...in a pinch if your child needs to stay home, on school/daycare closing days, or when another nanny is sick. They have been around for a long time and that's who I refer my friends who are parents (none in JP) to. I know families who have used them, including relatives. It was started by parents who needed "parent's in a pinch"...ie help.
Or...cheaper as I think there is no fee even for parents...is the website Care.com. Caregivers list their qualifications and write about themselves, that you can look through or you can post a job yourself. There is a background check function on that website as well. They also match elder care givers and pet caregivers with jobs in this way. As a caregiver (and I bet as a job poster too) you can arrange to get emails whenever a job (or applicant) matches your criterea. It's a great website (disclosure: I am on it!)
Probably by now you'd find someone but I'd thought I'd reply anyway. Best wishes