protected override void Render(HtmlTextWriter writer)
{
    MemoryStream ms = new MemoryStream();
    StreamWriter sw = new StreamWriter(ms);
    HtmlTextWriter htw = new HtmlTextWriter(sw);

    base.Render(htw);
    htw.Flush();
    ms.Position = 0;

    TextReader tr = new StreamReader(ms);
    string output = tr.ReadToEnd();
    string newOutput = ReplaceWithAppPath(output);
    writer.Write(newOutput);
    
    htw.Close();
    sw.Close();
    ms.Close();
}

public static string ReplaceWithAppPath(string str)
{
    string appPath = HttpContext.Current.Request.ApplicationPath;

    //Ensure the app path ends w/ a slash
    if(!appPath.EndsWith("/"))
        appPath += "/";

    return str.Replace("~/", appPath);
}