Counter into Legendaries?

I will count on my B/C Tyranitar and hope for a Houndoom with a good moveset.

For the birds I will use Golem with double rock and Tyranitar with SE.

For Mewtwo you will need dark type like B/C Tyranitar or maybe Umbreon with F/FF. Gengar is just too weak and takes SE damage from psychic.

Tyranitar all the way, Golem great for birds (though weak to Ice)

...a team of Tyranitar & Golem should be the top atm.
(against Mewtwo 6 Tyranitar? XD)

The biggest counter to any Raid Boss is the number of players.

Birds: I'd use the same moves as you suggested.

As for Mewtwo:
Gengar won't be a good counter to Mewtwo at all. Sure he deals SE damage, but he will also receives SE damage from Mewtwo's attacks. (if he has psychic moves at least)
Alakazam is to frail and can't deal STAB SE damage to Mewtwo (which I think will be important in raids battles)

A good counter I think will be Tyranitar with B/C. (or anny other dark pokemon with double dark moves) Deals SE damage and dark is immune to psychic in the main series games, which will get translated as x 0.51 damage received from Mewtwo's psychic attacks.

You will not want just one counter, but a team of six instead.

Focus Blast hits dark for super effective (140%) damage.

Gyarados and Arcanine have double dark movesets for Mewtwo, and better attack than Umbreon. Perhaps in time I would be happy that all my Garys have Bite, now that they're even worse defenders than before.

snorlax with lick/BS might be ok against the psychics as well (not as good as t rex) no special resistance but nice and bulky and good attack

I heard that "immunity" matchups have been added, and while not as potent as in other Pokémon games, the reddit did say it would reduce by about half

One word: tyranitar

From the sounds of it, Houndoom will be probably a good counter to Mewtwo being dark...We'll have to see how immunities work, but if it's near 0.5, that will make up a lot of the lower stamina Houndoom has...

T-rex is of course great, but it's harder to have 6 Tyranitars compared to pretty much an unlimited supply on Houndooms (230+ caught for me...). Very common in the desert areas...

For me, houndoor is pretty rare. Some discount counters include the double rock Golem you mentioned. For Mewtwo, double dark gyarados and double bug scizor are decent. Scizor has the same attack as Gary, but resists psychic and normal to help make up. Also, double bug gets STAB, so damage, depending on rounding. I realize scizor isn't the most "discount" but more so than tyranitar. A Bite/SE TTar may be a nice addition to any legendary attack party, with something for everyone, so to speak.