System.Text.Json（从 .NET Core 3.1 开始），为了能够序列化这些类型，您需要为JsonConverter<T>您需要的类型实现自己的类型并在JsonSerializerOptions. 为您要求的特定类型编写一个序列化程序应该相当容易。

如果您不想自己实现，有简便的方法，请参考另一篇文章：JsonException: A possible object cycle was detected which is not supported 检测到可能的对象循环，这是不受支持的-CSDN博客

适用于序列化的示例（省略了反序列化组件）代码如下：

public class DataTableConverter : JsonConverter<DataTable>
{
    public override DataTable Read(ref Utf8JsonReader reader, Type typeToConvert,
        JsonSerializerOptions options)
    {
        throw new NotImplementedException();
    }

    public override void Write(Utf8JsonWriter writer, DataTable value,
        JsonSerializerOptions options)
    {
        writer.WriteStartArray();

        foreach (DataRow row in value.Rows)
        {
            writer.WriteStartObject();
            foreach (DataColumn column in row.Table.Columns)
            {
                object columnValue = row[column];

                // If necessary:
                if (options.IgnoreNullValues)
                {
                    // Do null checks on the values here and skip writing.
                }

                writer.WritePropertyName(column.ColumnName);
                JsonSerializer.Serialize(writer, columnValue, options);
            }
            writer.WriteEndObject();
        }

        writer.WriteEndArray();
    }
}

public class DataSetConverter : JsonConverter<DataSet>
{
    public override DataSet Read(ref Utf8JsonReader reader, Type typeToConvert,
        JsonSerializerOptions options)
    {
        throw new NotImplementedException();
    }

    public override void Write(Utf8JsonWriter writer, DataSet value,
        JsonSerializerOptions options)
    {
        writer.WriteStartObject();
        foreach (DataTable table in value.Tables)
        {
            writer.WritePropertyName(table.TableName);
            JsonSerializer.Serialize(writer, table, options);
        }
        writer.WriteEndObject();
    }
}

private static void DataSet_Serialization_WithSystemTextJson()
{
    var options = new JsonSerializerOptions()
    {
        Converters = { new DataTableConverter(), new DataSetConverter() }
    };

    (DataTable table, DataSet dataSet) = GetDataSetAndTable();

    string jsonDataTable = JsonSerializer.Serialize(table, options);
    // [{"id":0,"item":"item 0"},{"id":1,"item":"item 1"}]
    Console.WriteLine(jsonDataTable);

    string jsonDataSet = JsonSerializer.Serialize(dataSet, options);
    // {"Table1":[{"id":0,"item":"item 0"},{"id":1,"item":"item 1"}]}
    Console.WriteLine(jsonDataSet);

    // Local function to create a sample DataTable and DataSet
    (DataTable, DataSet) GetDataSetAndTable()
    {
        dataSet = new DataSet("dataSet");

        table = new DataTable();
        DataColumn idColumn = new DataColumn("id", typeof(int))
        {
            AutoIncrement = true
        };

        DataColumn itemColumn = new DataColumn("item");

        table.Columns.Add(idColumn);
        table.Columns.Add(itemColumn);

        dataSet.Tables.Add(table);

        for (int i = 0; i < 2; i++)
        {
            DataRow newRow = table.NewRow();
            newRow["item"] = "item " + i;
            table.Rows.Add(newRow);
        }

        dataSet.AcceptChanges();

        return (table, dataSet);
    }
}

查看微软文档，可能会提供更多指导：

How to write custom converters for JSON serialization - .NET | Microsoft Learn

希望本文对你有帮助。