Revit doesn't have a DateTime parametertype. So you need to store the information in a different parametertype.
I would suggest using a Parameter of ParameterType.Text.
The exact format of the value-string, depend on your requirements.
Here are two possibilities.
DateTime time = DateTime.Now;
Parameter dateTimeParameter; // ParameterType == ParameterType.Text
DateTime value;
// human readable string
// set parameter.value
dateTimeParameter.Set( time.ToString("U"));
// get parameter.value
DateTime.TryParse(dateTimeParameter.AsString(), out value);
// alternative
// set parameter.value
dateTimeParameter.Set(time.Ticks.ToString());
// get parameter.value
long longvalue;
long.TryParse(dateTimeParameter.AsString(),out longvalue);
value = new DateTime(longvalue);