Hi,
EM Webservices API doesn't have any such functionality but have you looked into the possibility of using CLW (Command Line Workstation) ?
It supports querying\enabling\disabling Alert Downtime Schedules and since it's command based you can easily create a batch\shell to run and use cron job to automate it's execution.
For further details refer to APM Configuration Administration Guide- Using Command-Line Workstation Section.
Regards,
Kulbir.