You probably have been looking at some standard food oil, such as soy. There are much more viscous oils. For example, partially hydrogenated oils, used in products such as "Crisco", are so viscous that they seem like a sort of paste at room temperature. Probably you can just make a blend of hydrogenated oils and standard liquid ones to get the viscosity you want.
Mike W.
(published on 01/31/2015)