What if the Silence are on the Doctor's side?
Even I think this is unlikely, but it's worth considering. Maybe they had the child in the Day of the Moon to kill it or do something else with it. (They also said that Amy will bring the Silence. That never happened and we never actually found out what the Silence were planning to do). So, yes, maybe the Silence did try to blow up the TARDIS to stop the conception and the events of Day of the Moon were a sort of "plan B". They're ultimate goal may be to get rid of the Child, who is possibly River Song, who would be used as a weapon.