First, add one more field to your DesignEntity class. Whose type is the contract class that designDetails json is serialized from.
public class DesignEntity
{
    public string DesignName { get; set; }
    public string DesignID { get; set; }
    /// new field
    public DesignDetailsObject DesignDetails { get; set; }
    [ScriptIgnore]
    public string designDetails { get; set; }
}
And then, get your object as usual, deserialize the json first into that new field, then serialize it.
var designSessionEntity = new DesignEntity();
var jSerializer = new JavaScriptSerializer();
designSessionEntity = /// Get Values via some method
/// assign the design details with deserialized object
designSessionEntity.DesignDetails = jSerializer.Deserialize<DesignDetailsObject>(designSessionEntity.designDetails);
/// serialize it again
var designJsonSession = jSerializer.Serialize(designSessionEntity); 
Voila!
Update
If you don't have access to the class that designDetails json is serialized from, then you have two options.
- Try to deduce the class from the json structure and create the DesignDetailsObjectyourself (Recommended).
- Append the json string manually (I'll try to show you how if you need) - This method must be applied if the class is really heavy, and won't worth the work.
Code Snippet For option 2:
public string JsonAppender ( string targetJson, List<string> fields, object value )
{
    var insertIndex = 0;
    foreach ( var field in fields )
    {
        var _fieldDescriptor = field + "\":";
        insertIndex += targetJson.Substring(insertIndex).IndexOf(_fieldDescriptor) + _fieldDescriptor.Length;
    }
    var lengthOfDefaultVal = targetJson.Substring(insertIndex).IndexOf("\"") - 1;
    return targetJson.Substring(0, insertIndex) + "\"" + value + "\"" + targetJson.Substring(insertIndex + lengthOfDefaultVal);
}
Usage: 
var fieldAppendedJson = JsonAppender(json, new List<string> { "designDetails " }, designSessionEntity.designDetails);
     
    
string designJsonSession = "null";? You can just dostring designJsonSession = null;null- it is default value. Moreover, there is no need to split declaration and assignment up :)null.