Do Bryce's parents have reason to murder their son? Well, sort of. For starters, Nora has full knowledge of what her son is, and all but orders Chloe to break up with him and get an abortion, for her sake. Could she have been so disgusted she resorted to murder?
Toward the middle of the season, it's also revealed that Bryce has knowledge of his father's love child, which could seriously mess up divorce proceedings with his soon-to-be ex-wife. That alone is reason to kill him (coupled with the fact that Bryce's father doesn't seem to give a crap about him).
In the end, no, neither of Bryce's parents are the ones to kill him. Nora is actually well aware of her ex's love child, but decides not to use it against him in court, thereby eliminating Bryce's father's motive to kill him.