Sensitive eyes are easy to get irritation and infection. So people with sensitive eyes should avoid prolonged or extended contact lenses. The contact lens for a sensitive eye will depend on the cause for the sensitivity. So you should discuss your problem with your doctor.
Yes. There are some kinds of contatcs that are specially made for sensitive eyes. For example, Acuvue Oasys lenses are made with special technology for sensitive eyes. They will make people feel comfortable all day with the contact lenses in.
You can try Proclear Multifocal lenses. PC molecules attract and surround themselves with water, promoting an atmosphere where moist and comfortable contact lens wear is possible, cutting down on irritation due to sensitive eyes.