有两个问题我必须解决。第一个问题是如何序列化单个OleDbParameter。对于那个问题，已经有了@dbc指出的解决方案：
Newtonsoft.JSON无法转换具有TypeConverter属性的模型
对于OleDbParameter，我添加了以下内容：

[TypeConverter(typeof(OleDBParameterConverter))]
[JsonConverter(typeof(NoTypeConverterJsonConverter<System.Data.OleDb.OleDbParameter>))]
public class OleDBParameterConverter : TypeConverter
{
    public override bool CanConvertFrom(ITypeDescriptorContext context, System.Type sourceType)
    {
        if (sourceType == typeof(string))
        {
            return true;
        }
        return base.CanConvertFrom(context, sourceType);
    }
    public override object ConvertFrom(ITypeDescriptorContext context, System.Globalization.CultureInfo culture, object value)
    {
        if (value is string)
        {
            string s = value.ToString();
            //s = s.Replace("\\", "");
            System.Data.OleDb.OleDbParameter[] f = JsonConvert.DeserializeObject<System.Data.OleDb.OleDbParameter[]>(s);
            return f;
        }
        return base.ConvertFrom(context, culture, value);
    }
}

我添加了NoTypeConverterJsonConverter类

public class NoTypeConverterJsonConverter<T> : JsonConverter
{
    static readonly IContractResolver resolver = new NoTypeConverterContractResolver();

    class NoTypeConverterContractResolver : DefaultContractResolver
    {
        protected override JsonContract CreateContract(Type objectType)
        {
            if (typeof(T).IsAssignableFrom(objectType))
            {
                var contract = this.CreateObjectContract(objectType);
                contract.Converter = null; // Also null out the converter to prevent infinite recursion.
                return contract;
            }
            return base.CreateContract(objectType);
        }
    }

    public override bool CanConvert(Type objectType)
    {
        return typeof(T).IsAssignableFrom(objectType);
    }

    public override object ReadJson(JsonReader reader, Type objectType, object existingValue, JsonSerializer serializer)
    {
        return JsonSerializer.CreateDefault(new JsonSerializerSettings { ContractResolver = resolver }).Deserialize(reader, objectType);
    }

    public override void WriteJson(JsonWriter writer, object value, JsonSerializer serializer)
    {
        JsonSerializer.CreateDefault(new JsonSerializerSettings { ContractResolver = resolver }).Serialize(writer, value);
    }
}

这允许我序列化单个System.Data.OleDb.OleDbParameter，但我需要序列化它们的数组，我通过定义一个NoTypeConverterJsonConverter<System.Data.OleDb.OleDbParameter[]>来尝试

Newtonsoft.Json.JsonSerializerSettings oJSet = new Newtonsoft.Json.JsonSerializerSettings();
NoTypeConverterJsonConverter<System.Data.OleDb.OleDbParameter[]> oConv = new NoTypeConverterJsonConverter<System.Data.OleDb.OleDbParameter[]>();
oJSet.Converters.Add(oConv);

但是当我尝试使用它时，它导致了一个ArgumentException。
我最终发现可以通过将Array移动到System.Collections.Generic.List来避免这种情况<System.Data.OleDb.OleDbParameter>

System.Collections.Generic.List<System.Data.OleDb.OleDbParameter> oLParms = new System.Collections.Generic.List<System.Data.OleDb.OleDbParameter>();
foreach (System.Data.OleDb.OleDbParameter oParm in oParms)
{
    oLParms.Add(oParm);
}

这个，我能够序列化没有问题

Newtonsoft.Json.JsonSerializerSettings oJSet = new Newtonsoft.Json.JsonSerializerSettings();
NoTypeConverterJsonConverter<System.Data.OleDb.OleDbParameter> oConv = new NoTypeConverterJsonConverter<System.Data.OleDb.OleDbParameter>();
oJSet.Converters.Add(oConv);
sParameters = Newtonsoft.Json.JsonConvert.SerializeObject(value: oLParms, type: oLParms.GetType(), settings: oJSet);

反序列化也很容易：

oLParms = Newtonsoft.Json.JsonConvert.DeserializeObject<System.Collections.Generic.List<System.Data.OleDb.OleDbParameter>>(value: sParameters, settings: oJSet);
oParms = oLParms.ToArray();

非常感谢@dbc的帮助。