You'll need to write a custom converter to convert that DataTable to a JSON string. You can only tell JsonConvert how to convert types so you'll need to provide a converter for DataTable.
A DataTable is serialized as an array of objects with a property corresponding to each of the values in a row. You'll want to deserialize the JSON_Column column first so it is treated as an object and not a string. Once you created this new representation of your DataTable, you can let the serializer take care of the rest.
Here's how you could write such a converter:
Class MyDataTableConverter
Inherits JsonConverter
Public Overrides Function CanConvert(type As Type) As Boolean
Return type = GetType(DataTable)
End Function
Public Overrides Sub WriteJson(writer As JsonWriter, value As Object, serializer As JsonSerializer)
Dim dt = TryCast(value, DataTable)
If dt IsNot Nothing Then
Dim rowSerializer = New MyRowSerializer
Dim obj = New JArray(
From row In dt.Rows.Cast(Of DataRow)
Select rowSerializer.Serialize(dt, row.ItemArray)
)
serializer.Serialize(writer, obj)
End If
End Sub
Public Overrides Function ReadJson(reader As JsonReader, objectType As Type, existingValue As Object, serializer As JsonSerializer) As Object
If existingValue Is Nothing Then
Dim dt = CreateTable
Dim rowSerializer = New MyRowSerializer
Dim arr = serializer.Deserialize(Of JArray)(reader)
For Each obj In arr.Cast(Of JObject)
dt.Rows.Add(rowSerializer.Deserialize(dt, obj))
Next
Return dt
End If
Return existingValue
End Function
Private Function CreateTable() As DataTable
Dim dt = New DataTable
dt.Columns.Add("ColumnA", GetType(String))
dt.Columns.Add("JSON_Column", GetType(String))
Return dt
End Function
Class MyRowSerializer
Public Function Serialize(table As DataTable, values As Object()) As JObject
return New JObject(
From x in table.Columns.Cast(Of DataColumn).Zip(values, Function(col, value) New With { col.ColumnName, .ColumnValue = value })
Let value = SerializeColumn(x.ColumnName, x.ColumnValue)
Select New JProperty(x.ColumnName, value)
)
End Function
Private Function SerializeColumn(name As String, value As Object) As Object
Select Case name
Case "JSON_Column"
Return JsonConvert.DeserializeObject(DirectCast(value, String))
Case Else
Return value
End Select
End Function
Public Function Deserialize(table As DataTable, obj As JObject) As Object()
Dim values = From col In table.Columns.Cast(Of DataColumn)
Let columnName = col.ColumnName
Let value = obj(columnName)
Select DeserializeColumn(columnName, value)
return values.ToArray
End Function
Private Function DeserializeColumn(name As String, value As Object) As Object
Select Case name
Case "JSON_Column"
Return JsonConvert.SerializeObject(value)
Case Else
Return value
End Select
End Function
End Class
End Class
Then serialize your table passing in the converter as an argument.
Dim json = JsonConvert.SerializeObject(dataTable, New MyDataTableConverter)