Indian Mynah Birds

My first thought was a rat trap. Maybe try a mouse trap, they are a bit more sensitive. Might need to tie it down in case the bird flies off before it dies.

Or maybe fix the bait to the rat trap trigger somehow. Glue on a couple of grains of wheat or shove rolled oats under the little prongs so the bird has to struggle with the bait thus setting off the trap.

You might be able to trick them. Bait the rat trap but don't set it a couple of times. Bird comes in, gets bait easily a couple of times so loses caution, set the trap, SNAP.

Is poisoning an option?

They might go into a possum trap. I think they have a fairly sensitive trigger (can't remember).

Some sort of trap which is triggered by the bird's weight would work. Put the bait next to the trigger plate.

Borrow someone's terrier for a couple of days?

Commercially, LPG powered bird scarers are used. But they go "BOOM" to scare birds away so any close neighbours will hate you!

The local pest control mob might have some ideas.

A remote sentry gun or an automated tracking flamethrower is what the little buggers deserve. Good luck.