How can I trigger an event on an element in Polymer?

The correct way to trigger a click event is calling click() instead of onclick(), so the correct function would be

doClick: function(event, detail, sender) {
  console.log('Keypress event triggered');
  sender.click();
}

here is the JSFiddle Demo

You can also call the function instead of triggering an event if you are pointing the same element

Polymer('my-element', {
  clickEvent: function() {
      console.log('Click event triggered');
  },
  doClick: function(event, detail, sender) {
      console.log('Keypress event triggered');
      this.clickEvent();
  }
});

here is another JSFiddle Demo