If we drop the requirement that someone who is alive on the ship when it leaves Earth has to be alive when it arrives at the destination, it becomes much more feasible.
The basic idea is to combine two kinds of ship, neither of which we know how to make work individually, to form one that we can make work.
The first is the generation ship. The problems with those are that (1) we don't know for sure how to make a completely self-sustaining ecosystem that can keep a large enough population for viable colonization alive for the hundreds of generations it would take to reach their destination, and (2) such a population would require a freaking large ship, raising all kinds of challenges.
The second is the cryogenic suspension ship. The problem there is that we don't know how to unfreeze them without killing them.
Can we address the generation ship problems? Both problems stem from the need to have a large population. If we didn't need a large population, we could use some of the space that would have otherwise been consumed by colonist families to bring food to supplement the food produced by the ship's ecosystem, and eliminate the rest of the space they would have occupied.
Assume we can develop a food that can be stored indefinitely and that has the caloric density of rice (200 calories/cup). There are ~4 200 cups in a cubic meter, which gives 840 000 calories in a cubic meter. At 2000 calories per day, that's 420 days of food. A storage unit 10 meters on a side gives 1150 years worth of food for one person. And this is assuming that the person is getting all their calories out of storage, not depending on the ship's ecosystem.
If the storage food only needs to be a supplement designed to make up for things that we can't figure out how to get from the ship's ecosystem, then the numbers get even better.
This is where the cryogenic suspension comes in. We can't suspend and revive people--but we can do eggs and sperm indefinitely and revive them. Our cryonic generation ship will carry the colonists as frozen eggs and sperm. The only warm people on board would be the crew to operate the ship, and to raise the next generation crew.
Note that the next generation crew could come from the frozen eggs and sperm rather than from mating among the current generation crew, so we don't have to worry about a small crew becoming severely inbred during the trip.
If we can ever develop robots to the point that a robot can raise and educate a human baby without any human supervision, then we can leave out the crew and the food and the ecosystem, and just send robots plus frozen eggs and sperm.