I am looking for an air rifle to shoot pigeons and starlings inside of tin sheds on the farm. Shots will be 30 feet or less.

I need something to kill the birds but won't penetrate the tin if I miss. I would think a bb would be better than a pellet. Any advice would be great.

Anything that will penetrate deep enough into a pigeon to kill it will shoot through most thin steel roofs.  This goes for both bbs and pellets.

Now, choosing the right pellet and air rifle which will not go through both the bird and the roof is going to be a bit easier, but still kind of tricky.  To do this trick you are first going to need an airgun that is accurate enough to ensure that it will hit the birds each and every time. The good news is this may mean that you as the shooter are going to be the limiting factor as there are many airguns quite capable of doing this.  

For the pellet, I'd be inclined to choose something like the Crosman Premier Hollow point in either .177 or .22.  Though for me, personally, I like to use domed pellets but I am not as worried about pellets going through birds.  Whatever pellet you choose, you need to make sure that your air rifle likes the thing.  A pellet/rifle mismatch will cause misses and thus holes in the roof.

The rifle for the task is going to need to push the pellet out at about 650 to 700 ft/s.  No more than that.  This means that most of your box store spring air rifles are out of the picture.  Plus, spring airguns are generally more difficult to learn how to shoot well.   Pump air rifles like the Benjamin 392 give you the option of adjusting the power by how many pumps. Adjustable power PCPs like the Benjamin Marauder have the advantage in that you can get a lot more shots off in a shorter period of time and are quiet.  These do, however, require experimentation on getting the power to match the pellet and desired velocity.  At the velocity level you need you will get a lot of shot per fill.

One other very important consideration you need to understand is the trajectory at close ranges and elevated shots.  Failing here will result in a lot of misses.  The pellet starts off well below the line of sight, and is shot at a slight upward angle.  When shooting level the pellet will reach a maximum height at some range.  For many this is the sight in range where the pellet crosses the line of sight.  In your power level, this will be at about 25 yards for most scope heights.  The height of the sights above the bore are an important consideration here.  Iron sights tend to be a lot lower to the bore, and thus have a bit flatter trajectory at closer ranges.  

When shooting up, the trajectory from your point of view is going to be like if the target is closer to you.  It actually works out like you were to drop a plumb line from the target and shoot horizontally at the bob.

Scopes, or irons are going to be the next important choice.  Given the short distances, you may be better off with iron sights.  Unfortunately, the better PCPs do no have irons.  Many airguns that do have irons do not have very good ones.  Scope choices are going to require that you  have a close parallax/focus adjustment. It takes a bit of time to spin the focus know or ring to get the target in focus.  The target may move in the mean time.  If you do choose to use a scope, it needs a minimum focus distance of five yards or less.

Paint ball

Keep in mind the BB's will ricochet worse than a pellet.

I would go for a RWS 34 in 22.

I've shot plenty inside to. Sheds on my cousins dairy farm. The Tim they use is pretty heavy and I nsvwr out any holes in it with any of my guns.

When I shoot inside barns I use HN Match Heavy's, the flat face expands well but they tend to not penetrate roofs.   Use enough gun and they do the job on flying rats.

IMHO. Go get a paintball gun. Use a paper wad down the barrel. Add lead shot then cover with anothe paper wad. You have an air powered shotgun at that point.

Or you could just use frozen paint balls to shoot them

My best guess would be a pump rifle, which will let you calibrate for the sweet spot between killing a bird and not penetrating tin if you miss.  At 30 feet I would think you don't need something too powerful, and you can obviously test the power first to see where to start against the birds.

I'd recommend a break barrel 1000 fps nitro gun like the Crosman Fire NP. With a lesser guns, I kept getting broadside hits on the wing feathers on starlings and grackles at 15 yds and they get up and fly off. The Crosman did a number on them.

Of course, a head shot will work even with a red ryder,

At 30 feet, it sounds like you may get away with a paintball gun and chilled paint balls. Even these will bounce and deflect so wear protection.

A BB can both penetrate, and even worse ricochet efficiently, so I would strongly vote against BBs.

Soft flat head pellets from something like an R-7 using a dot scope or regular scope should do the trick if you don't miss. The small rat shot in the paintball gun trick works too, but you have to practice loading and shooting on paper till you get that worked out.

Again, wear protection if you are shooting near sheet metal.

Good Luck!