waswas-fng is correct, you cannot. One trick is to get site1 to send the cookie by having it display an image, say, from site2. (Then site2 actually sends the cookie.) You can even pass params to images if necessary! Consider: <img src="http://www.site2.com/images/foo.png?from=site1">
Of course, the image could be a 1x1 pixel image...