Rhode Island is cool with transport of an unloaded rifle; like most states RI has no state licensing requirements for the possession of rifles, shotguns, and handguns by adults.
OTOH, RI is weird about transport of handguns. As a non-resident without a RI permit, you can transport through the state non-stop, and from your "dwelling house" to the range, but can't bring a handgun to your friend's house if that is not your "dwelling house".