According to this patent - MEMS device using NiMn alloy and method of manufacture
US 7812703 B2 - it is between 30 and 60GPa for an alloy of about 0.01%
This paper provides information for a range of alloys - Dilatational Wave Velocities and Dynamic Elastic Moduli of Ni‐Mn Alloys - J. Appl. Phys. 36, 2666 (1965); http://dx.doi.org/10.1063/1.1714557
The literature will give you the typical range of values, but if you need a very accurate value, which is really specific to your own material (which has its own impurities and crystallinity), there is nothing else to do but measuring it by nano- or micro-indentation. You should find an access to such an instrument, and if you don't find, directly ask a supplier of such instruments for a free test of your material. This last solution, I would personally try it, and I indeed already successfully did in the past. Suppliers are always eager to prove that their instruments are able to do the measurements that you are intererested in.