I already have a recurring scheduled DND set for my phone for every evening through morning. However, I have calendar events that I would like to automatically trigger DND. For example, let's say I have a meeting with a co-worker, I'd like to be able to enter that into my calendar and select a "DND" option for that time. So, once the event is over, my phone is back to normal, and I don't have to worry about silencing it myself. Is this possible?
Short answer… No.
There is no public API that manages the "Do Not Disturb" feature. There are also no frameworks that can achieve this.
Googling would also say it's not the kind of sandbox breakout Apple would be likely to allow in the future, either.
This is a feature I find lacking in the current (and previous) versions of iOS. The only step one can take, unless one works on the iOS dev team @ Apple, is to give feedback about the iPhone, and make an enhancement request with this succinct need.
I did this months ago, and more folks who would like this functionality in later versions of iOS should make this request as well.