Is there an alternative to asking every civilization every turn for trade?

Almost every turn in Civilization 4 I cycle through all the other civilizations checking if they have any new technology or resource to trade.

This is time consuming. (I feel like going to war with them just to reduce the number of people to ask!)

Is there a quicker way of checking this?

Yes, there is. Check your diplomacy/foreign affairs advisor page, and it lists this information in a tabular format.

I know this might be a little late but anyhow.

Install a modpack such as bat mod here. http://civ4bug.sourceforge.net/BATMod.html

It contains features that don't change game balance, but makes it more convienient to play the game; in this case whenever a civilization has a technology they are willing to trade it will automatically show that info.