Cryogenics, when you get right down to it, is an attempt to slow Entropy, or the normal and constant use of energy in our bodies, which ultimately causes it to degrade. Extreme cold is useful for that because cold is essentially the absence of energy. Zero degrees Kelvin (-273 Degrees Celsius) is described as 'absolute zero' because at that point, there is a total absence of energy, and therefore nothing can ever get colder than that. (Deep space is around 3 degrees Kelvin)
The problem with cryogenics for complex organisms is that most molecular materials, as they cool, form solids and actually shrink in size. Water, on the other hand, expands as it gets colder. Water at 4 degrees C is actually denser than ice.
This is why ice cubes float in your glass of water (or Scotch, etc.).
For the purposes of cryogenics, given that complex life forms are 70% water, this effect can essentially tear cells apart.
There are some notable exceptions in nature. The Tardigrade, or Water Bear, is a small, multicelluar organism that can replace its water content with a form of sugar molecule to survive freezing temperatures and reanimate. There are even a small number of turtles, snakes and Frogs that can survive naturally freezing temperatures for extended periods through some natural form of cryogenic suspension. From this alone, we know that it's possible, but we have a long way to go before we can say that this is even a viable technology for space flight.
That said, humans (after a fashion) are already being cryogenically suspended and reanimated as a part of common medical practice. In-Vitro Fertilisation (IVF) treatments and other forms of artificial insemination rely in some cases on either frozen eggs (ova), sperm, or even Embryos that are stored in cryogenics, 'thawed' and placed back in a viable host. So, it's even possible with some human tissues as a part of existing medical practice.
The real issue is that the protective chemicals that allow certain cells to survive the freezing process are at present quite toxic as well. This means that large, thicker tissue samples, like hearts, livers, complete human beings, etc. still don't have viable recovery methods after freezing, and in some cases during freezing. Also, we've never asked a Tardigrade or a Spring Peeper if how much they remember after their freezing, and whether or not they're really still 'themselves'. The suspension and reanimation of a complex human mind with its suite of memories and 'soft', programmable set of practices (cerebral cortex) has never been tested completely and even if we can solve the biological problems, we really don't know what it would do to a complex mind just yet.
So; as I see it, in the not too distant future, there are really two possibilities that could make cryogenics plausible;
1) Development of some cryoprotectant chemicals that are NOT toxic to human life (and by that I mean both biological and neurological)
2) Development of a different kind of entropy suspension method that somehow locks out energetic interaction with the universe without reducing localised energy levels (ie; making it cold).
Of these 2, I think (1) is the most plausible, but what that chemical might be I don't know. I guess if I did, I'd be making a fortune right now, but I digress.
The answer to your question is NOT the design of a new freezing model; we have that pretty much perfected. It's the design of a new chemical or water molecule control process that would allow for ice not to expand without the treatment that allows this to happen being toxic. From a world building perspective, the place I'd start would be the tardigrade and the relevant species of frogs, snakes, turtles etc. that can survive freezing and see if there's something plausible in their natural design that can be applied to a near future state to humans.
