I would say that the answer to this question lies principally with the person who is praying, since God is outside of time, and is always ready to hear us, wherever or whenever we might pray.
Therefore, I would say that a specific time of day that an individual devotes to prayer should be on a case-by-case basis, or even on a day-to-day basis, based on those times (whenever they may be or occur) that would be most conducive for that individual to set aside other concerns, and to focus his or her attention completely and solely on prayer, without the problems or distractions of day-to-day life intruding (except to the extent that the individual may be lifting them in prayer to God).
I would also say that the individual should be careful to keep regular prayer from being transformed into a rote ritual that over time becomes something that is performed at fixed times or in a fixed manner just for its own sake, without real attention or thought being devoted to it.
I agree that we should pray any time and as Paul states: "Pray without ceasing" ( 1 Thessalonians 5:17 ). We should maintain a continual, prayerful attitude.
However, much can be said for morning prayer. Overnight sleep not only refreshes the body but also the mind. Before becoming encumbered with daily activities and bogged down with problems that arise, there is nothing that can compare to spending this quiet time with the Lord.
I've personally found that an "early" submission positively affects my whole day. "[[A Psalm of David, when he was in the wilderness of Judah.]] O God, thou art my God; early will I seek thee: my soul thirsteth for thee, my flesh longeth for thee in a dry and thirsty land, where no water is;" ( Psalms 63:1 ) "I love them that love me; and those that seek me early shall find me." ( Proverbs 8:17 ) "With my soul have I desired thee in the night; yea, with my spirit within me will I seek thee early: for when thy judgments are in the earth, the inhabitants of the world will learn righteousness." ( Isaiah 26:9 ).
"And Abraham gat up early in the morning to the place where he stood before the LORD:" (Genesis 19 :27) I'm not aware of a specific verse that says "pray in the morning" but do a word/phrase search for early, rose up early, morning, etc. In many instances those greatly used of God were early risers. Www.blb.org is a good tool for searching. "And early in the morning he came again into the temple, and all the people came unto him; and he sat down, and taught them." ( John 8:2 )