There are plenty of private kindergartens all over SLU, easy to find, and a free playground for children belonging to Pizza Pizza in Rodney Bay, behind 'Delirious' restaurant, for the past 10 years or so.
The best way to get your first nanny in SLU is to contact the local employment agencies from the telephone directory at http://stluciayp.com/
I do not know if the nannies whom the agencies have on their lists are bonded & insured but at least the employment agency has their personal data on record.
Another idea is to publish a WANTED ad in The Voice newspaper for EC$47 http://www.thevoiceslu.com (The Voice is the oldest & largest circulated newspaper and the weekend edition is best for all ads).