I try not to catch my birds during the day unless it is necessary**. I do showmanship with my birds, so I handle them as I would in a show. I do this by putting my hand under their body with my pointer finger on their chest bone and my thumb on one side of the body and my other three fingers on the other side. That way when they start to flap I can hold to them and have control. (if it helps I can post some pictures)
**My chickens are cool with being handled, but catching them is hard so I wait until night and they are in the coop so I can catch them. There is the exception of the aggressive rooster who if I need to lock up because he ain't being nice then I tell our dog to "go get the chickie-chickie" He will flip the rooster on his back and holds on to him and waits until I take the nasty boy
 
The holding the bird up side down will only kill the bird if done improperly (we have to do that in showmanship) If you do it right then everyone will be ok