High-Viscosity Lubricant

if the cover closes of it's own weight they commonly use a hydraulic cylinder or air cylinder that opens freely and as it closes it then pumps the air or fluid through an adjustable aperture. You can get light weight ones to close screen doors that use air. The heavy duty closers use a fluid. Another way is a pully set with an adjustable crimp brake on one of the pulleys.

Damping grease inhibits free motion and quiets the noise associated with metal-on-metal, metal-on-plastic, or plastic-on-plastic devices. A staple in automotive controls, stereo tuners, camera zoom lenses, and microscope focus mechanisms, Nye's family of damping grease is a cost-efficient way to build smooth, controlled, quiet motion - a "velvet feel" - into mechanical and electromechanical devices. This is from; http://www.nyelubricants.com/damping.php?section=Lubricants-SpecialtyProducts-DampingGrease

Look at silicone oils they are more stable in temperature (less change versus temperature) than mineral oils and one can mix them to required viscosity. I think dow-corning is a supplier. use google for search.