Can you buy Daedric / Dragon Bone armour?

Is it possible to buy these armours or is smithing the only way to get them?

Solution 1:

No, outside of finding them as random loot, smithing is currently the only way to obtain these sets of armor. You cannot buy them from any shops.

Solution 2:

I'm at level 40 and have just found daedric boots as random loot so it's definitely possible to find them outside of smithing.

Solution 3:

There are two ways to get them outside of smithing - You could perform the conjuration ritual spell (req. Conjuration 90) from Phinnis at the College of Winterhold which rewards you with a sigil stone.

That stone is used to upgrade the Atronach Forge in the Midden underneath the college. That forge allows you to make either unenchanted Deadric armor and weapons or enchanted ones

The other way is only applicable if you have the Dragonborn DLC; open the black book Untold Legends and at the end choose the black market power. You can then summon a Dremora merchant that, if you have the right level, will sell Daedric.