I bought two pieces of land. One from Morthal, and one from Falkreath. Morthal was the first plot of land I purchased. I only finished half of it. I bought the plot of land in falkreath because I liked the nature better. I finished the house completely in Falkreath. Every time I try to adopt a child off the streets it keeps saying "I have a place but no room for you" Even though I have the bedrooms in my Falkreath house. Why can I not adopt a child and have him/her live at my house in Falkreath?
In order to adopt children you need to put in two childs beds AND the childs chests. You have to have the chests too otherwise it won't work :) That's what happened to me, if that didn't work then I literally have no idea, try and adopt homeless children (like in whiterun or windhelm) instead of the orphanage.
All you have to do is have the chests & the beds. Single beds work as well if you don't have the Bedrooms addition to your house. Just make sure your children have either the child beds + the chests or single beds if you have no Bedrooms addition. I freaked out too when I couldn't adopt a child. Time passed and my husband and I lived in a half decorated house. I asked my house steward to finish decorating the house. After the rest of the furniture came that I was too lazy to get the materials for, I talked to an orphan in the street of Whiterun. I decided to see if now, since the house was finished if I could adopt her. So, I looked, and it was an option. Simple as that. ♥
It could be a glitch in your game, but I can assure you its most likely because you don't meet the requirements... meaning you don't have two beds and two chests in a children's room. Sometimes, like in my game, I had a glitch where it wouldn't let me adopt a child until I had a wardrobe as well as the beds and chests. Also, I recommend trying to adopt children from the street, and then try the orphanage. I had a problem quite like yours, and I solved it by doing this: ask homeless kid that wanders the streets, then an orphan kid, and then a homeless kid again. At the second homeless kid try, I was able to ask the kid to come live with me and was able to have the child as my own. ...I hope this does help, friend, and may you be successful in getting your child. <3