Two more real theories I remember reading on the forums:

After finding JR molesting JBR, Patsy went out to the garage and got her tire iron out of the trunk to hit JR, but missed and hit JBR instead. She was unable to dispose of the body because she had locked her keys in the trunk.

Patsy found JonBenet eating pineapple and got so mad she hit her over the head with a flashlight, then put her on her new bike and pushed her down the stairs to the basement.