You might say that it's because I am a morning person that prayer in the morning is most meaningful to me. I think the reasons are deeper. Morning is a beginning, morning is renewal, and the Bible recognizes this time and again.
Many believers offer a prayer as close to their waking moment as possible, the moment when they know they will stay awake. Traditional prayers come to the mind, such as the "Gloria Patri":
"Glory be to the Father, and to the Son, and to the Holy Spirit. As it was in the beginning, is now and ever shall be. World without end, amen."
Or: "In the name of the Father, and the Son, and the Holy Spirit."
You might just let the first phrase from the Bible that comes to your mind be your prayer upon awakening. Many of the passages associated with the morning work beautifully, with phrases marked in bold that might come to mind:
Psalm 57:7: "My heart is steadfast, O God, my heart is steadfast! I will sing and make melody!
8: Awake, my soul! Awake, O harp and lyre! I will awake the dawn!
9: I will give thanks to thee, O Lord, among the peoples; I will sing praises to thee among the nations.
10: For thy steadfast love is great to the heavens, thy faithfulness to the clouds.
11: Be exalted, O God, above the heavens! Let thy glory be over all the earth!"
Lamentations 3:21: "But this I call to mind, and therefore I have hope: 22: The steadfast love of the LORD never ceases, his mercies never come to an end;
23: they are new every morning; great is thy faithfulness.
24: "The LORD is my portion," says my soul, "therefore I will hope in him."
25: The LORD is good to those who wait for him, to the soul that seeks him.
Psalm 19:1: "The heavens are telling the glory of God; and the firmament proclaims his handiwork. "
Psalm 27:1: "The LORD is my light and my salvation; whom shall I fear? The LORD is the stronghold of my life; of whom shall I be afraid?"
Psalm 65:8: "Those who live at earth's farthest bounds are awed by your signs; you make the gateways of the morning and the evening shout for joy."
Psalm 119:18: Open my eyes, so that I may behold wondrous things out of your law.
Psalm 143:8: "Let me hear of your steadfast love in the morning, for in you I put my trust. Teach me the way I should go, for to you I lift up my soul."
See what I mean?
Of course, the first phrase that comes to mind, your first prayer, need not be one that talks of the dawn. There are so many others, each of which can serve as a motto for the whole day. There is Isaiah's offer:
Isaiah 6:8: "Then I heard the voice of the Lord saying, 'Whom shall I send and who will go for us?' And I said, 'Here am I; send me!'"
Our very model of faithfulness is Mary, who in her response to the angel Gabriel said: Luke 1:38: "Here am I, the servant of the Lord; let it be with me according to your word."
Let your first conscious thought in the morning be prayer.