Only six men signed both documents, but god is not mentioned anywhere in the Constitution, and despite what you would have us believe, there's a reason for that.  However, almost four dozen signatories of the DOI (in which god is explicitly mentioned) owned slaves. So does your 'line of reasoning' suggest that they thought they had a god given right to own slaves?  "rights...derived from God."  Ha, ha..pray tell us what rights were derived from god, maybe "thou  shall not covet thy neighbor's servants", which in those days would of course have been slaves.