Below is a beautiful prayer, written by Elder Paisios the Athonite, of Blessed Memory (+1994), for monastics to pray every evening on behalf of the world. This is meaningful because it underlines that the purpose of monasticism is not for monks or nuns to solely pray for themselves, but demonstrates to laypeople that their goal is to pray for and support the whole world. This also illustrates the great love that the Elder had and continues to have for all those who suffer from any trial or temptation throughout the world. He helped many multitudes of people on a daily basis through his prayer and instructions, and helps even more after his repose. Finally, as mentioned in the short introduction that I have also translated below, this could definitely be a suitable prayer for laypeople to say on a daily basis, helping us to entreat Christ on behalf of the whole world.
The love of Elder Paisios for the whole world is well-known. The Elder has helped a multitude of people, both before and after his repose.
From where did he receive the power to strengthen people, and to work miracles? From his fervent prayer to God.
The following prayer was given to a women's monastery which had asked him for some "typikon" for their vigils in their cells. This is from one of the last years of his life. In this can chiefly found his love for the whole world.
This can be used by each of the faithful, as it covers all cases of people who have need of prayer. Even children can understand it, and it is written in simple words, and thus can be read during the family's evening prayer.
From the book, "God is with us, are we with Him", by Orthodox Kypseli. (Amateur translation of text from Source)
***I do not believe it would be impious to also include a special prayer for your country or place of origin.