Dionysos also governs the theatre, so writing a short play dedicated to Him would make a suitable offering, or if your talents as an actor are better than a writer you could perform a short excerpt from a Classical play, such as Euripdes 'The Bacchae'. Dithyrambs were hymns of praise sung to Dionysos so if you enjoy singing and/or can write songs this is another option.
Wine and mead have been mentioned but you can also offer any kind of alcohol as well as ivy, vines, figs, oakmoss and various kinds of musks.
If you are artistic you can make masks in a Greek Theatre style, or a thysros, which is a staff made of a fennel stalk wrapped in ivy and tipped with a pine cone. These can be kept on a shrine or given up as offerings.
I'd also suggest checking out http://www.wildivine.org/dionysos.htm for more Dionysian bits and pieces.