Spring rate is a function of geometry as well as material. That's probably why you're not finding material-based comparative values. For gross comparisons, the ratios of the elasticity moduli is of the same order as spring constants for parts made of different materials.

The best online source of material properties that I'm aware of is www.matweb.com

Thanks you have confirmed my suspicions, I thought it was the geometry that was holding me up and I had been using modulus of elasticity instead.

Nice to check these things though

The axial stiffness of a prismatric member is EA/L, where E is the elastic modulus in unit of force per length square , A is the cross section in unit of length square and L is the length.  The combine unit is therefore always in force per unit length.  

In simple terms, force equals spring constant times deflection (F=kx) for an axially loaded bar.  Hence, both the material properities and geometry influence the spring constant.

The spring constant concept above is the basis for the finite element or matrix methods of structural analysis.

I go along with 1969grad's way of description of the spring constant concept.

I even would venture to say that it is the mother of all computer methods of structural analysis.  

Structures are longer solved by complicated differential equations but are simulated as small springs (with rotational and torsional stiffness thrown in if appropiate).  The power of the computer is to assemble the springs faithfully according to our instructions (nodal coordinates and member connection etc) and solve tediously a huge number of simultaneous equations for the deflection on receiving the loading information.  If we have to do it by hand to solve the same huge number of simultaneous equations it can take us a life time just for one structure but the computer can do it before you finish reading this post.

The computer treats a structure as one huge spring except that it has many sub-springs able deform in many directions.  We put load in it and out go the deflection.  
100 times the load will turn out 100 times deflection. (unless it is a specialised software written for nonlinear or inelastic analyses). Luckily the computer does not know when the structure fail and that is where the engineer fits in.

The axial spring constant EA/L is always found on any structure member and is the simplest of all stiffness terms.