Why can't I adopt children?

Adoption have requirements :

• Having a house with a child bedroom or a second room in a self-built house.
• Finishing the Innocence Lost quest

As you said, you have the bedroom.

Have you finished the Innocence Lost quest ?

Since you've completed the house requirements, here are the other thing you need to do:

1. You need to complete Innocence Lost by going into the Arentino Residence and talk to Aventus. After it's complete, later go back and talk to the lady Constance. I know you're trying to adopt from the orphanage.

If you still can't adopt from the orphanage, you can adopt the other following children: Lucia from Whiterun, Blaise from Solitude, Sophie from Windhelm, and Alesan from Dawnstar.

If nothing works, download the Hearthfire Unoffical Path which fixes some things in the game depending on the DLC pack.

So all you have to do is head to rifton and kill the other caretaker, after that go to the western watchtower and press X (If you have an Xbox remote) This enables an elder dragon to fly by, follow the dragon in flight until you reach theives guild hiding place and ask for the guild members to help you defeat the dragon (It will cost you) and head back to the orphanage, (it should be on fire because of the dragon) and you should be able to get an orphan for free.