Pretty much every stall team I've witnessed and encountered has had something to stop the birds, something to wall Scarf Sawk (mesprit / missy), something to halt Gorebyss (Jynx) a (or multiple) hazard setter(s) and cryogonal to spin away the opponents hazards.
In terms of stopping Swellow, Braviary and Fearow I've seen pretty much every steel and rock type plus the hybrids in order to fulfill this role on the team. Regirock, Probo, Lairon, Golem and Omastar all have the ability to easily set up Stealth Rock after walling each bird and a plus in Omastar's case is he can also lay spikes, too. The more roles you can perform with each mon the better.
Scarf Sawk is a pretty interesting case because he can easily tear through the aforementioned rocks with a simple Close Combat, and being able to wall both Swellow and Sawk takes some good prediction to avoid double switches and such. The added disadvantage is that Swellow can easily U-turn to predict Regirock coming in and bam you're facing Sawk while Regirock took damage from U-turn. Interesting options in order to make this pinch hurt as little as possible are Mesprit (who can rock for you if you'd like, or set up screens, a whole multitude of crap), Misdreavus (who with an Eviolite is one of the bulkiest mons in the tier and can kindly perish trap or sleep something in order to releave stress from Swellow Sawk Cores) and finally Tangela, who has a really fitting niche because with an eviolite and maximum investment in HP and Defense fails to be 3hko'd by Swellow's Brave Bird AFTER ROCKS. Tangela can sleep powder, toxic and physically stall out everything with physical attacks that isn't boosted to insane levels (I mean even absol has trouble with him).
Gorebyss is an interesting case because it's one of the few special sweepers in the tier, she really only shares this with SubNP Jynx and Specs Exeggutor, who really is just there to systematically rape anything that switches in with leaf storm and then leave in hysterical laughter. There are quite a few special walls to note to take care of all three mons (or atleast two of them handily). Cryogonal, Mantine, Jynx, Quagsire and Lapras all can safely take on Gorebyss depending on the hidden power she runs (Grass or Rock). If Grass, everyone but Quag and Lapras can handle her while if she runs HP rock Lapras and Quag can both handily Stall her out (note: Quaggy has been dropping in usage lately so its effectiveness is kind of questionable). Exeggutor is really there to just Leaf Storm the fuck out of things but he does pack coverage moves in order to check his weaknesses, that doesn't exactly mean he's perfect though. Cacturne can easily switch in on Leaf Storm or Psychic and proceed to scare him out and set up sub and spike for you. Skuntank can also switch in on psychics and trap eggy with pursuit. Zwelious resists all three of Eggy's moves but is a bit too offensive for a stall team. Altaria is also a nice option against eggy, only fearing psychic, and she can perform well as a cleric and general wall with her respectable 75/90/105 defenses and access to Cotton Guard (Bulky late-game sweeper potential). Articuno, Arbok, Drifblim, Rotom-S and Wormadam-Trash can all switch in on a variety of Eggy's moves and threaten it back with their respective attacks.
Garbador, Whirlipede and a few other previously mentioned mons can all set up spikes, t-spikes and stealth rock in order to help you wear down your opponents team. In league with stalling via hazards it would be good to pack a spin blocker or an effective way to deal with a spinner (Cryo mainly but Wartortle and Starmie have popped up lately). Misdreavus does this job easily and can support the team by perish trapping or paralyzing any threats to the rest of the team and more importantly, keeping hazards up. You don't really have to worry about spinners because of the evident lack of them (if omastar got rapid spin I'd jump on it in a heartbeat), but it's always a good idea to prepare for anyone running a balanced team. I guess it's your call, though.