Drink a glass of water. You will not be able to chirp without a lot of saliva or water in your mouth.
Pool a small amount of saliva or water on your tongue at the back of your mouth and try to whistle gently while holding it there. The air should pass over the liquid and make a quiet gurgling or warbling sound.
Loosen your lips as you whistle, allowing them to vibrate as the air comes out your mouth. This combined with the warbling should produce a chirp similar to that of a cricket.