Dohnányi Ernő (western name Ernst von Dohnányi) was a Hungarian composer who lived from 1877 to 1960. In addition to his music, Dohnányi also wrote three volumes of Essential Finger Exercises. While the collection is marketed towards a pianist with a few years of experience, some of the easier exercises can definitely be useful to somebody who has only been playing for a couple of years.
Why Dohnányi? In the words of the author himself:
When playing, even the simplest of finger exercises, the full attention must be fixed on the finger-work, each note must be played consciously, in short: not to practise merely with the fingers, but through the fingers with the brain.
(from the Preface to Essential Finger Exercises, translated by Norah Drewett)
Dohnányi's exercises are intended to make one think actively when they play. Because of this, many of them are structured differently than other technique exercises, like Hanon or scales. While it is always better to have a keyboard, a few of these exercises can be played on a tabletop.
Of the 40 exercises Dohnányi wrote, the first seven are probably your best bet for practicing without a keyboard. These seven exercises focus on individual finger strength, and don't move around the keyboard at all. They are all played by holding your fingers on/over the same five keys and playing various patterns. For example, Exercise No. 2 is a traditional "five-finger pattern," only you practice holding down one finger while the other fingers continue to play up and down (try it, it's harder than you think!).
These seven Dohnányi exercises are my go-to thing when I've got a little bit of time, but I don't have access to a piano. Since I started them, my agility and finger independence has improved noticeably.
To make the most of your practicing, Dohnányi recommended playing his exercises hands apart, then hands separately. He also recommended practicing "forte with all possible strength, slowly and with well raised fingers, as well as piano in a more rapid tempo." All of these instructions can be done on a tabletop, as long as you maintain good posture and wrist position. In addition, I would add practicing with a keyboard as often as possible, since a tabletop (obviously) doesn't have the same touch as a piano.
Another thing you lose with tabletop practicing is the height/distance difference between black and white keys. This means you can only practice things in C, which limits the effectiveness of what you practice. When you do get a chance, run through your technique exercises (scales, arpeggios, Dohnányi, etc.) in various keys so that you can keep a feel for all the keys.
In the end, what matters most is how mentally engaged you are in your practicing. Just tapping out patterns with your fingers won't do you any good if you aren't focusing on what you're doing. 10 focused minutes of finger work will benefit you much more than a half hour of "practicing" while your mind is somewhere else. Especially since you don't have a piano in front of you to help keep your attention on one task, you will need to focus on whatever you are practicing if you want that practicing to be effective.
The less time spent on purely technical studies, the more important it is to practise with full concentrated thought. It is absolutely useless to practice exercises in a thoughtless, mechanical manner, especially when the eyes are riveted on the music.
– Ernst von Dohnányi (Preface to Essential Finger Exercises, translated by Norah Drewett)
As far as finding a copy of Dohnáni's exercises goes, they are still under copyright, and unfortunately not in the public domain, at least in the U.S. You can find them on Amazon here, and I'm sure they can be found other places as well.
