Are shops and markets in Yogya (Marlioboro) and Solo ((Batik markets) open on Sundays?
Thanks!

of course they do!
Not sure what you can buy in Marlioboro as it is pretty much touristy in nature.
Indonesia's shoppingscene is a 7 days a week business and also go far beyond the western shoppinghours. Yes touristy stuff on Malioboro but you can buy almost everything there including clothes, shoes, electronics, vcd's, eateries and batik. Solo also has an interesting antiquemarket (well if you are interested of course).
Have fun, your backpack or suitcase will be too small at the end of Malioboro (but no worries, this stuff is on sale as well)
Anne Mieke