All centres I have seen have a big on the door of each room that says:

(insert number here) cases of (insert illness here) reported in this room in the last (insert number here) weeks.

Maybe suggest that your centre does something similar so that parents know if gastro/flu/hand,foot& mouth/conjunctivitis etc is going around so that they can be aware of it and maybe NOT send thier kids to childcare if they look like they have symptoms.