The following situations can cause eye watering:
1. Contact lens damaged;
2. Wearing contacts inside out;
3. Eye infection
For the first one, you should buy a new contact lens. For two, wearing lens correctly. If your eye is infected, you'd better take an appointment with your optician. And you cannot wear lens till your eye get healed.
Sometimes there is a small rip or puncture in the contact that you may not see. Or, you could have contacts that do not give your eyes enough oxygen. Sometimes if you don't rinse or do your overnight cleansing well enough it causes your eyes to sting and water. If you want to try a different brand of contacts talk to your doctor and tell him your symptoms and he/she could probably supply or recommend a different brand or contacts. Good luck with them. All of these have happened to me before and they were all somewhat easy fixes.
Have you ever checked your eyes to judge whether you are suitable to wear the contact lenses? Some type of people with eyes dieases such as the trachoma, cataract, glaucoma are not suitable to wear the contact lenses. Your eyes keep watering when wearing the contact lenses must be caused by the irritating stimulation. You'd better have a check on your eyes.