First it should be noted that there's no guarantee the birds will return to T5 raids (at least anytime soon). The odds of this happening will decrease further should they be confirmed as quest rewards.
For Articuno, Entei is probably the best of the recently-released lot, with Raikou a close second. Others you could look at are Lunatone, Solrock, Blaziken, and Metagross.
For Moltres, Kyogre has to be up there, while Rayquaza with Ancient Power would also pack a punch. Raikou is a solid option here. Lunatone and Solrock, again, would be decent.
Finally, for Zapdos, Raikou would actually make a solid counter, resisting electric-type moves but dealing regular damage (since Zapdos doesn't resist electric-type offense). Other than Raikou (and a generalist like Rayquaza), however, I feel you'd be best off with the same old faces for this one.
Shoutout to Mew for being a decent counter for any and all of the three given the appropriate moveset.