sur l'ordinateur, no good?
I've seen it used but it might be taken as "I tap on the computer". To say "Je tape à l'ordinateur", it is clear what is meant.
Still not accepted.
Wasn't sure whether it was à or sur, checked on Google Translate, and of course DL won't accept sur (which GT suggested).
I type on the keyboard. Though maybe it is laptop,keyboard is usually on top of the computer there...