cry on (one's) shoulder
To bemoan one's problems to someone else. We need to try to cheer Ben up—he's been crying on my shoulder all week. Can I please cry on your shoulder for a little bit? I just found out I failed my Bio exam.
cry on someone's shoulder
Tell one's problems to someone so as to gain sympathy or consolation, as in When James had a problem at the office he generally cried on his sister's shoulder. It is also put as a shoulder to cry on, as in When Mom came home, Jane had a shoulder to cry on. [Late 1930s]
cry on (someone's) shoulder
To tell one's problems to someone else in an attempt to gain sympathy or consolation.