Tell Json.Net to write a single-quote rather than a double quote when serializing objects

Yes, this is possible. If you use a JsonTextWriter explicitly instead of using JsonConvert.SerializeObject(), you can set the QuoteChar to a single quote.

var obj = new { key = "value" };

StringBuilder sb = new StringBuilder();
using (StringWriter sw = new StringWriter(sb))
using (JsonTextWriter writer = new JsonTextWriter(sw))
{
    writer.QuoteChar="\"';

    JsonSerializer ser = new JsonSerializer();
    ser.Serialize(writer, obj);
}

Console.WriteLine(sb.ToString());

Output:

{'key':'value'}

Fiddle: https://dotnetfiddle.net/LGRl1k

Keep in mind that using single quotes around keys and values in JSON is considered non-standard (see JSON.org), and may cause problems for parsers that adhere strictly to the standard.