CaCO3 has a couple of interesting properties in pH 7 DI water:

• Sparingly soluble leading to dissolution and changes in both size and surface
• Usually possessing a positive zeta potential at this pH

As you indicate stabilization is key.  From a scientific perspective you can measure the zeta potential and then use an optimum level of an ionic additive to provide stabilization.  Alternatively a steric stabilizer could be used.  For a general overview and a simple vial route to indicate stabilization see slides 45 onwards in:

Nov 11th, 2008. Dispersion and nanotechnology http://tinyurl.com/hpywsge

My first try would be with differing levels of PO42- additive remembering that too much is as bad as too little.  The amount you need for monolayer coverage will depend on the surface area (and thus on the particle size)

Dear Mike and Alan,

thanks for your comments. I am going to try PO42- and polyacrylic acid soon.

I must have mentioned a crucial point which I forgot: We already have a suspension of CaCO3 particles in hand (so we are not synthetizing) with aggregate size of ca.1000nm. We also have tried humic acid, which leads to Zeta Potential of promising range (-40mV), but the suspension is not stable, which is because the humic acid is not coating the particles, it is just in solution reducing the Zeta potential.

At 300 nm you'll have increased absolute solubility and rate of solubility for CaCO3 - one would expect to see size reduction in this regime until CaCO3 saturation in the surrounding phase.  In what way are you claiming the suspension is not stable?  ZP is a holistic property of particle and medium it resides in  - you must have something coating or adsorbing  on the particle surface to alter the ZP.  You may be able to alter the pH somewhat to more alkaline noting that lower pH's favor dissolution with evolution of CO2.  How are you measuring the size and the ZP?