Like in Singapore, a lot of people can afford maids at home and therefore making child-care and baby-sitting easier. You can find kindergarten everywhere for different prices and different services.
Here is an example:
Alison's Letterland Child Care Centre / International Kindergarten with web site.
For more info see also in the school section.
There is also Gumtree: go to education section for ads about teaching and home services for education.
Otherwise most hotels in Hong Kong also provide with baby-sitting services but the best way still remains by word of mouth.