The second one is correct; the first one almost but not quite: relaxivity r describes how the relaxation rate R (1/second = 1/s = s-1) changes depending on the concentration c (mmol/L = mM = millimolar) of the contrast agent; "1 molar = 1 M" is an abbreviation for "1 mol/L = 1 mol/litre".

So, relaxivity is change of relaxation rate divided by change of concentration, i.e. r = dR / dc with the units: (1/s) / (mmol/L) = s-1 mmol-1 L = (1/s) / mM = s-1 mM-1 = L / (mmol s).

Of course, the concentration can also be given in mol/L = M or any other multiple of this.