The Treaty of Tripoli from 1796 specifically states "As the Government of the United States of America is not, in any sense, founded on the Christian religion,—as it has in itself no character of enmity against the laws, religion, or tranquility, of Mussulmen [Muslims],—and as the said States never entered into any war or act of hostility against any Mahometan [Mohammedan] nation, it is declared by the parties that no pretext arising from religious opinions shall ever produce an interruption of the harmony existing between the two countries."

Not sure if you brought it up, but the Treaty of Tripoli was submitted by Adams, passed unanimously by the Senate, and then signed by Adams. It says "As the Government of the United States of America is not, in any sense, founded on the Christian religion,—as it has in itself no character of enmity against the laws, religion, or tranquility, of Mussulmen [Muslims],—and as the said States never entered into any war or act of hostility against any Mahometan [Mohammedan] nation, it is declared by the parties that no pretext arising from religious opinions shall ever produce an interruption of the harmony existing between the two countries."

I'm not sure how much more explicit you can get.

Personally, there is two different arguments that I would use. The first is that not all the founding fathers were Christians. Men like Thomas Jefferson and Ben Franklin were deists, and it would be pretty out of line for them to found a nation based on a religion they didn't believe in (Source: http://www.monticello.org/site/research-and-collections/jeffersons-religious-beliefs, http://www.portal.state.pa.us/portal/server.pt/community/history/20018/benjamin_franklin_and_his_religious_beliefs/1014592). Then there was guys like Thomas Paine, who was pretty much against all forms of organized religion (Source: http://www.fordham.edu/halsall/mod/paine-deism.asp). Yes, Paine usually isn't thought of as a founding father, but he is a significant individual in the war of independence, and his ideology and stance on religion should not be discounted. Even a lot of the founding fathers, like George Washington, weren't exactly religious zealots. Washington was low Anglican, which meant that he was more liberal in his religions beliefs; it is debatable whether or not he even took communion(Source: http://www.mountvernon.org/educational-resources/encyclopedia/george-washington-and-religion). In short, the idea that the founding fathers were a bunch of God-fearing Christians doesn't hold up to scrutiny.

The other argument that I would use is The Treaty of Tripoli. It's a more technical and obscure argument, but I feel that it is usable. The only history that you need know about the treaty is that it was ratified by the Senate in 1797 and the President who signed the treaty was John Adams, a founding father. The section that we will be focusing on is Article 11. Article 11 states:

"As the government of the United States of America is not in any sense founded on the Christian Religion,-as it has in itself no character of enmity against the laws, religion or tranquility of Musselmen[Muslims],-and as the said States never have entered into any war or act of hostility against any Mehomitan[Muslim] nation, it is declared by the parties that no pretext arising from religious opinions shall ever produce an interruption of the harmony existing between the two countries. " Source: http://avalon.law.yale.edu/18th_century/bar1796t.asp

The first sentence alone indicates that America wasn't founded as a Christian nation. Now the issue is that the translation between Arabic and English was sketchy at best. However, it is important to remember that the quote above was what congress and Adams read; it doesn't matter what it originally said in Arabic, what matters is what it said in English, which is what the quote above states.

Edit: Sources and spelling