Serializing A Class To Place On Confluent Schema Registry

I'm attempting to manually register a schema with Confluents Schema registry calling RegisterSchemaAsync.

I've attempted multiple methods of serializing my class, including newton soft json schema and confluents json serializer, but they don't seem to be in quite the right format.

The newtonsoft one seems to give the closest to what I'm after:

        JSchemaGenerator generator = new JSchemaGenerator();
        JSchema schema = generator.Generate(typeof(TotallyCoolCustomClass));

        var subject = "TotallyCoolCustomClass"; //Assuming we want to use the Record strategy
        var stringSchema = schema.ToString();
        var schemaId = await schemaRegistry.RegisterSchemaAsync(subject, schema.ToString());

Provides:

'Invalid schema {subject=TotallyCoolCustomClass,version=0,id=-1,schemaType=AVRO,references=[],metadata=null,ruleSet=null,schema={
  "type": "object",
  "properties": {
    "FavouriteQuote": {
      "type": [
        "string",
        "null"
      ]
    },
    "FavouriteNumber": {
      "type": "integer"
    }
  },
  "required": [
    "FavouriteQuote",
    "FavouriteNumber"
  ]
}} with refs [] of type AVRO, details: Type not supported: object; error code: 42201'

Any suggestions on how I can serialize a class definition into the right format for the schema?

Ended up using NJsonSchema.

var schemaRegistry = new CachedSchemaRegistryClient(schemaRegistryConfig);

            var schema = JsonSchema.FromType<TotallyCoolCustomClass>();
            var schemaData = schema.ToJson();

            var subject = "TotallyCoolCustomClass"; //Assuming we want to use the Record strategy
            var schemaId = await schemaRegistry.RegisterSchemaAsync(subject, new Schema(schemaData, new List<SchemaReference>(), Confluent.SchemaRegistry.SchemaType.Json));