Rabbi Tovia Singer provides deeply welcoming teachings regarding the necessity of Jews to welcome others to pray as a Jew. I agree with Rabbi Singer.
Jews are called to be a light unto the nations, and to me, that includes being a light in prayer. I pray with people who are not Jewish, and they pray with me.
Essentially, a Noahide Jewish prayer is one which acknowledges God as Creator, thanks God and humbly makes requests of God, the same way Jewish prayers do. No intercessor is involved between the person praying and his or her Almighty God. That is monotheism and that is the foundation of Jewish personal prayer as well as communal, traditional prayers.
Fifteen minutes into the following 2016 video (this link is set up to begin at 15:00) you'll hear Rabbi Singer's unforgettable explanation about the responsibility of Jews to serve as a light to the nations with their Jewish prayer. He is answering questions posed by this man, a Noahide who believed he was not welcome to pray as a Jew. Those days are over for him now, and hopefully for all of B'inei Noach and others worldwide!
As Rabbi Singer tells him, and all of us watching, "Everyone who is created in the image of God MUST pray like a Jew."