I am not quite sure I understand your question. A Cooper pair is a pair of correlated electrons one with spin up one with spin down such that the resulting quasi particle, the Cooper pair, becomes a Boson while the constituents, the electrons are Fermions. The coupling happens in conventional superconductors via virtual phonons. The mass of a Cooper pair is therefore basically the mass of two electrons if that is what you mean. If you mean by density of superconductor the density of the superconducting material then the contribution of the Cooper pairs to the mass is completely negligible. 

Dear Binek

Thank you for your kind reply. In fact I have developed an electrodynamics model for superconductivity taking into account London's theory. This model is based on an extended electrodynamics(Maxwell's equations) where an additional scalar (boson) bears the properties of Cooper pairs. This scalar is found to satisfy the Klein-Gordon equation. The charge and current densities are found to be related to this boson that is also governed by Euler equation reflecting a fluid nature of this scalar. As a result the equation of state of this fluid is that due to non-relativistic fluid satisfying the equation of state  P=1/2 rho v^2. Moreover, the mass and pressure densities of this fluid are found to be proportional to the charge and current densities squared.

I see, then please ignore my rather naive answer. I am afraid, I can't comment anything you may find useful. 

A very good question, Arbab. A  little bit of care must be exercised  in interpreting the Cooper pairs as localized bound electrons. Actually the electrons in a  Cooper pair  are separated both in time and space. So, they are not local pairs and accordingly one must interpret the notions of charge and mass densities.

On the other hand, p-wave pairing (as in strontium ruthenate) and d-wave pairing (as in the cuprates) may have quite different mechanisms and quite different kinds of superconducting bosons.  Those in the cuprates are positively charged for hole-doped materials and negatively charged for electron-doped materials.  "Bosonization" (the theory of which is quite beyond me, I hasten to add) can produce peculiaritites like "holons" (spinless charged quasiparticles) and "spinons" (chargeless quasiparticles with spin).  Even charge is not simple -- recall the fractionally charged quasiparticles in the Fractional Quantum Hall Effect. 

My point is, you must beware of thinking about superconducting charge carriers in terms of the same elementary particles (with well defined charge and mass) that exist in "normal" vacuum.  In any highly correlated electron material, you should think of the host as an alternate vacuum with different (but potentially understandable) "laws of physics", and the "particles" in that material as the low-lying excited states of said vacuum.