What are some of the character conflicts in Coraline?
The main conflict is Man versus Society. Coraline, as a young child, has a specific role to play in society, but she is dissatisfied with that role. She is bored with her summer; there is no school to keep her mind busy, and so she explores. She feels that her father and mother are not attentive enough, but they feel that she should keep herself quiet and not bother them while they are working. Everything that follows in the book is a result of Coraline pushing back against both societal roles and authority; she refuses to listen when she is warned not to open the small door in her wall.
Coraline stopped and listened. She knew she was doing something wrong, and she was trying to listen for her mother coming back, but she heard nothing. Then Coraline... opened the door.
(Gaiman, Coraline, Google Books)
Her refusal to listen to authority leads her into trouble, but it is also what allows her to overcome each obstacle. By remembering the advice of her elders, and understanding the advice as it pertains to the strange events of the book, Coraline is able to survive and win.
There are also examples of Man versus Man (such as Coraline versus the Other Mother) and Man versus Nature (such as Coraline trying to navigate thick mist and escape strange creatures).