Yes, Beerus has been shown to be upset to the point where it could be interpreted as crying.
During the Tournament of Power in Dragon Ball Super, Beerus displayed significant emotional distress when it appeared that Goku had been defeated by Jiren after using the Spirit Bomb. While not explicitly shown with tears streaming down his face, the Dragon Ball Wiki notes that Beerus was visibly upset and mournfully said Goku's name, implying a deep concern for Goku's well-being and a sadness at the prospect of his demise. This instance suggests that Beerus is capable of experiencing a level of emotional vulnerability that could manifest as crying, even if it's not always explicitly depicted.
