We're having a sunroom and it's going to get a lot of...sun! Will more sunlight make the carpet have a shorter life? Will it discolor the carpet? Finally, is there a kind of carpet you would recommend for the sunroom? Which types of carpets will be best fit for this type of room?

You have a sun room? Are you in Riyadh, Saudi Arabia? If so,how much 'sun' do you need in a room in Riyadh?

Or do you sell carpets to Westerners for them to put in their sunrooms?

If you need advice on the effects of sun on carpets, why not ask around where you are? Everyone (apart from you, oddly) in the capital city of a Desert Kingdom where carpets are important culturally and are manufactured , must surely know.

On the off chance that this is an earnest question- Yes, if you use traditional wool,silk or flax for your sunroom floor covering, the sun will destroy it in a matter of 2 or 3 years, even if the rug was created to last ten generations.

For this use, I would recomend jute, bamboo, or any one of several man-made fibers- many available now are made entirely from recycled materials.
If you'll do an internet search for "Outdoor Rugs" you'll find a wide variety of floor coverings suitable for use in a sunroom, solarium or patio.