It's surprisingly hard to research what poisons are actually good to use, you'll either gets sites shilling stuff that completely doesn't work, but is "eco friendly" (for example "Rat-X"), and sites that simply give you the "most effective", i.e. most poisonous (like the ones in this article).
What's needed are sites explaining, for an average person, what's they should be getting. People aren't trying to kill birds, they just are getting really bad advice on what to buy.
Bromethalin is a good choice, if you use a bait station (it has no antidote, so always use a bait station, never just tie the blocks somewhere).