All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Yes, it is permissible for a person to supplicate Allaah to bless him to cry out of fear of Him because crying out of fear of Allaah is something desired in Islam, and the person who cries out of fear of Allaah is promised that his eyes will not be touched by fire on the Day of Judgment, and that Allaah will shade him under His Shade on the Day of Judgment.
Therefore, if a person supplicates for this, he has indeed supplicated for something desired and encouraged in Islam.
The lack of crying out of fear is due to our hearts being hard. The righteous who cry out of fear of Allaah, it is because they have good hearts. The heart is the controller of all other parts of the body, and if the heart is good, all other parts, among which are the eyes, will be good.
Hence, we should be concerned with our heart and endeavor to purify them from the filth of sins, desires and misconceptions. It is at this stage that the heart will be filled with the fear of Allaah, glorify Him and fear His Punishment and hope for His Reward, and it is at this time that our eyes will shed tears without effort.
We ask Allaah to rectify our hearts, purify them and bless us to cry out of fear of Him.
Allaah Knows best.