I have heard that crafting Dwarven bows is generally the best way to raise smithing now, but what if you are only perking the light armor side of the tree? How do you raise your smithing skill effectively?

I don't know that dwarven bows are the best way, but they are probably close to the most cost effective item you can smith, provided you're strong enough to brave Dwemer ruins for the materials and have the time. The higher the value of the item you create, the more XP it will give you.

There is an alternative to putting perks down the heavy armour path though. If you pick up the transmute ore spell, you'll be able to make jewelry 'en masse'.

Gold jewelry is the most cost effective, at least in my experience. Get the transmute spell and every cheap piece of iron ore is now gold. You can craft jewelry with or without jewels so you don't even have to worry about extra 'pieces' needed.