Is there any way to stimulate eye-tear production in order to treat dry eyes?

Tear production: The only treatment been shown to increase tear production is Restasis (cyclosporine 0.05%). Many other treatments for dry eye can be effective so i would recommend seeing an eye doctor to ensure proper evaluation and treatment.

Dry eyes!: All of the following will help. Creating a more healthy environment will help promote more tear production. Start with artificial tears routinely (one drop 4 times a day every day), oral omega-3's, and warm compresses. Next, medicated drops (restasis, mild steroid drops, NSAID drops) or punctal occlusion may be helpful.