You should be able to distribute a seed for Random(int seed) and recreate the same sequence assuming that you are using the same version of .NET in all environments.
Remarks on System.Random @ MSDN
Notes to Callers The implementation of the random number generator in the Random class is not guaranteed to remain the same across major versions of the .NET Framework. As a result, your application code should not assume that the same seed will result in the same pseudo-random sequence in different versions of the .NET Framework.
If you can see a case where the framework version will change, or if you may need to recreate an old sequence after you've started using a new version, you'll want to create your own random implementation.
See the answers of this question for pointers: Crossplatform random number generator