Day care in Hong Kong is rare for young babies/ toddlers, as most working women hire a domestic helper to care for their newborn, and go back to work shortly after the birth. They then place the baby in these two hour sessions, once the helper or Mommie can accompany the growing toddler.
I would suggest applying now for September, for the kindergarten/ nurseries that appeal to you. The places are already allocated for this coming academic year, but I have no doubt that some will consider late applications.
http://www.chsc.hk/kindergarten/
The following kindergartens seem to have nurseries which I believe may be suitable for your baby's needs.
Would you consider local cantonese day care? If so, the following organisation, and the supervisor/ headmistress of the school is superb, in my opinion.
CARITAS NURSERY SCHOOL - KENNEDY TOWN
FLOOR 2, BLOCK A, 1/F (PORTION), M1/F (PORTION) &, 2/F OF BLOCK B, CARITAS SOCIAL CENTRE KE, 27 POKFIELD ROAD, KENNEDY TOWN, HONG KONG
CARMEL SCHOOL (Jewish Hebrew School)
FLOOR 3&4, 70 ROBINSON ROAD, MID-LEVEL, HONG KONG
Best of luck!