Off market trading is always available... you can do private agreements (I guess) over the weekends.
IG Markets (a CFD provider) makes a market for Sunday trading in a few major indices. http://www.ig.com/au/sunday-trading I haven't looked at it closely but at a guess the spread would be quite wide.
Some online betting firms may offer bets related to financial markets... so they are kind of imperfect ways to trade.
So there are a few ways to manage your market exposure over the weekend... none of them are particularly efficient for obvious reasons.