Dan Phillips has asked some people this question. See here for more details.
Theologian John Frame says he would do it only on the condition that he would be allowed to pray in Jesus’ name, and that he would pray something like the following:
We pray to you our creator, the mighty king of kings and lord of lords, who governs all things that come to pass and rules over all the nations. You raise up rulers and cast them down at your own pleasure, in the pursuit of your just and merciful purposes. We thank you for the freedom we have to worship you, sought by the founders of this nation, freedom you have given to us through the righteous laws of this land. So we call on you to be with us again during this new era. Be with our new president and all the leaders of this country, that they may be willing to hear the wisdom of your word and thus may image your justice, mercy, and integrity in their public life. As the one who remains constant throughout history, and yet who ordains change from each moment to the next, move our leaders to know how to maintain the foundations of our nation, while changing to meet the demands of new situations. Be our rock, when so much is changing in our lives. We pray for those families whose loved ones have died in defense of our country, and we pray for the young men and women who continue to fight our battles, that they may be victorious, and that their efforts may bring about the fruit of peace. We pray for those who have experienced terrible losses through the changes in the economy, and we pray that the leaders of this nation may seek out the wisest ways of responding. Above all, pour out on this nation your Holy Spirit, that there will be revival in our land, that the hearts of many will be moved to seek you, and that they may find that new life you offer us of love, joy, and peace.
This we pray in the name of Jesus Christ,
What will you pray for our president?
HT: JT