Disabling alarms at given times

I've got a backup WAN connection that goes down for some sort of self-test every day at exactly midnight and then comes back again a few seconds later. The test is in the hardware and can't be disabled.  What this means is that every day I get two Internet Connectivity Update alerts a few seconds apart.

Is there some way to disable specific alerts on a schedule?  In this case I'd like to disable connectivity alerts between 23:59 and 00:01, but others have asked for something similar in the features forum.