Archenland: Since Archenland is described as a mountainous country with many types of trees, I thought metal ore and timber would be two things they'd export. The strong wine is directly mentioned in VDT as a provision Caspian brings on the ship.
Calormen: Members of the Calormene aristocracy seem to be dripping in jewels (i.e. the Tisroc) and the country seems to contain many foods not really mentioned elsewhere (Almonds, Figs, Oranges, Melons and Lobsters). Tarkaan Anradin's beard is coated in scented oil, and Lasaraleen vacations at the "Valley of a Thousand Perfumes".
Lone Islands: Since Felimath is a place where lots of sheep grazed, it seemed logical that wool would be a major export. Fiefs are mentioned on Avra, and one of the principle crops of fiefs in the Middle Ages was grain (wheat, rye, barley ect...) Doorn was tricky, but I don't recall ale being mentioned (unless you count "beer") elsewhere in the Chronicles.
Narnia: Silk is mentioned several times as a Narnian produ