Some parents...
telecommute
use the drop-in daycare available at their company/employer
hire an on-call nanny through a local agency
pass their child to a friend's nanny for the day (pay for a one-day nanny-share, essentially)
call on neighbors/friends/family in the area for help (I've seen friends posting on FB looking for last-minute childcare)
consult Craigslist for available carers (not exactly recommended)
take a day off from work or split a half-day off from work with their partner (Parent #1 home in the morning, at work in afternoon, Parent #2 the reverse)
Sadly there are no miraculous suggestions that you haven't thought of already, just the regular challenge of arranging childcare in a country that isn't child- (or parent-) friendly.