It seem like Sunday mornings and times vary on when I have seen the new ones. At times it has been when I get up, so pretty early and other times it has been noonish.
Check out this blog site, she also has an email subscription www.totallytarget.com. From what I've learned, print them when you have the chance as they may be gone the next time you get around to it.
I just tried to print a Pace picante sauce coupon from there a few days ago, never got one to print and it kept saying that I had already printed the max number of times. So sometimes they don't even work! Good luck