Examples of invocation prayers include the Invocation of the Holy Ghost, First Prayer of the Continental Congress in 1774 and invocations during a graduation ceremony. The U.S. House of Representatives Chaplain, Catholic.org and living prayers offer many examples on their websites.
The Invocation of the Holy Ghost prays that all nations become unified by faith in the Lord. Other prayers listed on the site include Invocation for the Faithful Dead, A Countryman Gives Thanks and Invocation to the Most Holy Name of Jesus.
The U.S. House of Representatives Chaplain archives many of the invocations that have been made prior to the start of proceedings. Prayers are found with a search using a combination of month and day or session of Congress.