Storing liquified gasses is a solved problem. The auto-industry at least has been experimenting with Liquid Propane Gas for a while, without issues. Actually most automobiles in Turkey run on LPG.
Hydrogen is a slightly different animal, colder temperatures, and more explosive. We know the materials that will work, we know how to produce them. Its more of an engineering/production/economy of scale issue then anything else.
The pressures need to be higher, which means stronger and more expensive tanks. It also means we must input more energy to compress the gas for storage.
Hydrogen is also significantly smaller and more reactive than NG. Which also means the tanks are more expensive as they need to be resistant against corrosion. Additionally, the valves and seals in the system need to be of a higher class as hydrogen is more prone to leak.
Can't keep the car in the garage.
Maybe it would be possible to store the liquid and release the hydrogen only when it is actually going to be used.