Why can't I adopt kids despite already having killed Grelod the Kind?

Solution 1:

You can adopt kids,there's one in katlas farm (Blaise) and one who usually sits next to the tree in whiterun (Lucia).Theres a few more (1 in every hold atleast) Happy child hunting!

Solution 2:

First, you must go to Windhelm and talk to Aventus Aretino.

He will reward you for killing Grelod. After this, you will receive a letter from a courier, from the Dark Brotherhood. This begins the quest "With Friends Like These...."

After you get this note, sleep in a bed. You will be abducted by the Dark Brotherhood. After this, you either need to join the Brotherhood or kill Astrid.

After completing this, you should be able to adopt children.

Solution 3:

After you are inducted into the dark brotherhood, you can get them. Steps below

1: get inducted

2: become thane, and build your house

3: go to the orphanage and adopt a child (after you get the letter stating that Michele has taken over the orphanage)

MAKE SURE YOU HAVE A HOUSE BUILT WITH CHILDERN'S BEDS TOO, OR YOU CAN'T ADOPT A CHILD