Oh man. That's a big question. There are simply too many Avialan Dinosaurs that don't get enough attention.
I know you specifically asked for Cenozoic, but I'm also going to take the time to highlight some great Mesozoic Avialans, because they also never get any attention
Mesozoic Avialans Worthy of Attention:
I know they bounce back and forth a lot because there isn't actually a dividing line between "dinosaur" and "bird", but I have to mention the Anchiornithids - Things like Caihong, Serikornis, and of course Anchiornis itself are really cool fluffy friends that really showcase the variety of feather adaptations
Jeholornis is amazing, we know so much about it and its ecology! It ate seeds, it had a rad tail, it just is aesthetically pleasing
I love Sapeornis because it was essentially the first "bird of prey" if we don't count Microraptor (which admittedly we could)
Confuciusornis is possibly one of the best known Mesozoic dinosaurs of all time. Where the hell is it. Why isn't it in literally anything. Amber Isle even has the tail of Confuciusornis as an option for your character, but gd forbid having an NPC be one I guess
Enantiornithines. There are so many of them. It's kind of insane. Like, these non-Neornithine dinosaurs were essentially *the* birds of the Cretaceous period. I can't even cover all the ones that deserve attention, not fairly anyway. Off the top of my head - Shanweiniao is a great one, as is Bohaiornis, and Gobipteryx, and Avimaia is a wonderful specimen, and Avisaurus is a big hit for Hell Creek fans, and Falcatakely is literally the Tooth-can, and Imparavis was toothless and that's cool, and Lectavis was very like modern shorebirds, and Parvavis is the smallest known Mesozoic dinosaur, and Chiappeavis had a cool tail fan, and I should really stop before this gets too long
On the line to modern birds, Patagopteryx is an early example of a bird that re-evolved flightlessness! I mean yeah things like Utahraptor are too but shush
Yanornis is just such a cool transitional species
Gansus is actually well known for a reason - it was aquatic!
Can you really go wrong with Apsaravis?
Literally the entirety of Hesperonithines
Ichthyornis is just Platinum Tier
And then we have the earliest "modern birds", which are Mesozoic! We've got Vegavis (probably) and Asteriornis! Showcasing how even in the Cretaceous, we had Chickens (ish) and Ducks (ish)
Cenozoic Avians Worthy Of Attention:
Gastornis. Gastornis. Gastornis. Gastornis.
PELAGORNITHIDS. these weirdos responded to the problem of "birds can't reevolve teeth" with "LETS JUST MAKE OUR BEAKS LOOK RIDICULOUS" and they were successful throughout the Cenozoic and just died out bc of the ice age and thats the only reason we don't have any?????? and NOTHING USES THEM??? besides ark which is a travesty
There's a whole score of interesting birds that are in the Passerine-Parrot group but not proper Passerines or Parrots that I've dubbed "Pass-Parrots of Prey" (formerly Parrots of Prey) because they're all raptorial! parrots and passerines come from raptor ancestors!
apparently frigatebirds did the Gull thing before they were frigatebirds and before gulls existed and that's Limnofregata
PENGUINS. They show up RIGHT after the end-cretaceous and have a detailed Paleocene fossil record (a rarity, I assure you) - so we have a great transitional sequence and then on top of it some are HUGE
I deeply love presbyornithids
Sandcoleids are little weirdos I love them
LITHORNITHIDS. They are the base from which Paleognaths evolved and they were flying friends!
Terror Birds. They show up early in the Cenozoic and only died out at the end of the Ice Age. they were a HUGE component of South America's ecosystems and were extremely successful. Also, badass.
Bathornis is basically the North American terror bird (ignore Titanis) so that too
qianshanornis is a cutie with a sickle claw
PLOTOPTERIDS! some booby relatives were like "we want to be penguins" and then they did it! in the northern hemisphere! they were all over the Pacific!
Dromornithids (Mihirungs) are super cool Australian megafowl
I'm a little biased, but I think the screamer-duck I helped described (Anachronornis) is pretty cool
I love Palaelodids (Swimming Flamingos) because they just look Weeeeeeird
I have a soft spot for Zygodactylids because they're basically the usual passerine body but with parrot feet. that's rad
Teratorns were cool vulture-relatives that got REALLY big
There are a handful of terrestrial raptors related to falcons that were notable in the Eocene like Danielsraptor
I deeply appreciate Moa and Elephant Birds for being big friends
Haast's Eagle is one of those things you shouldn't think about too hard
Xenicibis and your club-wings my beloved
Heracles was a Giant fucking Kakapo/Kea/Kaka type parrot and it was RIDICULOUS
I'm ignoring a lot of transitional birds - early members of different groups that tried out unique niches or ecologies that their modern relatives don't do - because if I listed them all this post would get ridiculous. just trust there's tons of interesting small birds that require more text to show how they're interesting than I feel like writing at 5am
Sylviornis was another excellent Megafowl
z''l dodos and great auks
Talpanas, aka, the Reverse-Platypus