Jeremy I've had the pleasure to have a variety of net throwing devices in my handed at one time or another.
I would love to own them all if money and need wasn't an issue.
The smallest contained unit might have done it for you it is the "talon" that is advertised fairly widely for our industry
animal control agencies and even police dept folks.
It is the cheapest entry level system that will expel a net with a small gas charge.
I've attempted to use this in real situations multiple times and the take home I have is if the species isn't fairly stable on the spot you
will literally spend more time trying to retrieve the net from whatever it can tangle on.
If your quarry is in it awesome and worth it, if not just a time suck.....
The larger net guns that use .308 blanks are widely used from aerial operations for large cervids and carnivores etc.... Can still be used for smaller fowl and fare but throws some serious weights and like any of those from there up they cost some serious bucks and you can behead or kill your quarry with the weights. Happensore often than folks like to admit.
The talon has small weights and is like a flashlight in size.
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Now I'm going to winkleman on this post before someone says it...
No one tried "pretty bird, pretty bird" to get it to come down?

Just had one here that folks called into the city we contract for. Many folks saw it but not possible to reach it.
I agree with evertt and stated so here as well, if you don't retrive it a coopers hawk will soon enough....
Justin