Updating parent and child records at the same time

We have a situation where the application updates a child record and based on that change there is a change to the parent table's status_id column. There is a trigger that is supposed to handle this, but we are getting deadlocks when users are updating the child in the application because we are trying to update both of these at the same time. Is there a way to commit the change in the child and get the parent updated with the correct status at the same time? Thanks!

UPDATE child_table SET ...;
UPDATE parent_table SET ...;
COMMIT;