Although the morning time is itself reminds a Muslim the remembrance of Allah, yet it is recommended to dua at morning for the sake to remember Allah just after saying Fajr prayer and before sun rise. It is narrated in Al-Hakim hadith No# 2000 and he graded it authentic, in Ath-Thahabi agreed and, Sahih At-Targhib wa At-Tarhib No# 661 as,
 

Translation

O Ever Living, O Self-Subsisting and Supporter of all, by Your mercy I seek assistance, rectify for me all of my affairs and do not leave me to myself, even for the blink of an eye.
 

Alternatively Recite This

  أَصْبَـحْـنا وَأَصْبَـحْ المُـلكُ للَّهِ رَبِّ العـالَمـين ، اللّهُـمَّ إِنِّـي أسْـأَلُـكَ خَـيْرَ هـذا الـيَوْم ،

فَـتْحَهُ وَنَصْـرَهُ ، وَنـورَهُ وَبَـرَكَتَـهُ ، وَهُـداهُ ، وَأَعـوذُ بِـكَ

مِـنْ شَـرِّ ما فـيهِ وَشَـرِّ ما بَعْـدَه

Translation

The morning has come to me and the whole universe belongs to Allah, the Lord of the worlds, O Allah, I ask of you the good of the day, it's success and aid and it's nur (celestial light) and barakaat (blessings) and seek hidayah (guidance) and seek refuge from the evil in it (this day) and from the evil of that which is to come later.
 

Alternatively Recite This

Translation

O Allah we enter the day time and the evening and die with your Qudrat (power) and to You do we return.