i think it's risky telling them you don't want sundays
you can say it's for religious reasons, they *should* be ok with that because they are equal opportunity employers, but what happens in practice isn't the same as in theory. if they said weekend availability is a must you probably have to stick with it.
to cut is short, i think it's too much of a risk to say you can't work every sunday, especially when you're new. (i am assuming you don't have religious reasons though, i can't tell from your posts)