There are many LEGO customizers who do custom printing, however please note that all printing makes sense only if hundreds of the same design are requested. Otherwise there is quite a bit of work involved with designing, formatting, color-matching and aligning each print. However if you have the money and willing to pay a few hundred bucks set-up fee for each design, there are options.
Please note that most LEGO customizers won't be willing to do exact replicas of LEGO's own design, as it is illegal to reproduce and sell them.
You might be better off getting water-slide decals, and even designing them yourself. The end result looks almost the same as direct printing on elements, although they will be more delicate.
If you are interested to get your own printer for LEGO pieces they are called pad-printing machines. They are expensive, but prices are coming down, especially on used ones.