In C# you can use the following to replace the single quote with a double quote:
string sample = "St. Mary's";
string escapedSample = sample.Replace("'", "''");
And the output will be:
"St. Mary''s"
And, if you are working with Sqlite directly; you can work with object instead of string and catch special things like DBNull:
private static string MySqlEscape(Object usString)
{
if (usString is DBNull)
{
return "";
}
string sample = Convert.ToString(usString);
return sample.Replace("'", "''");
}