I want to encourage this greeting for the first day of the week. There is a greeting for Sunday that I heard a good bit in Italy: "buona domenica." I think that is where I got the idea. It seems to me that "Happy Sunday" is a good English equivalent. Sunday really should have its own special greeting, as it is a special day.
For Christians, of course, Sunday is a special day. I am not so sure how special Sunday is in our culture anymore. At Vanderbilt, Sunday is study day par excellence. I often have students ask me about studying so much on Sunday: does it violate the sabbath rest? I don't think it does, and I kind of like Sunday being such a day of the intellect. Intellectual work was never considered to be servile labor, the kind that violated the sabbath; but I don't want to get into a discourse/dispute about the sabbath. I am mainly using this as an example of how Sunday is still different for some of us.
The main way that Sunday ought to be different is the happiness of the day. It is the day of the resurrection, of the new creation. It is the pre-eminent day of worship. So whatever we choose or have to do on Sundays, let's be happy and worship. For me, during the school year Sundays are kind of grueling. Starting one of the main events of the day at 9 p.m. makes for a long day, especially since I still begin pretty early. But I love Sundays. There is something to them that is different. I find a finality on Sunday night that can't be beaten.
So, whatever your day holds for you: Happy Sunday!