What did the spartans trade
Spartans did not trade anything. There was a law in Sparta that banned all foreign trade and foreign travelling. This reserved out all foreign ideas and allowed them to have the element of surprise when it came to attacks. Go to http://www.studyworld.com/newsite/reportessay/history/european%5Csparta_vs_athens.htm for details.
Perhaps Iron, copper, bronze. Food products like grapes, olives, figs. Linen, timber, certain naval store products like pitch, that were used in "greek fire".