How would one say, “We are triumphant while our enemy sleeps.”? Gratias vobis ago!
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Here is a simple suggestion:
Inimicis [nostris] dormientibus triumphamus.
We triumph while/when/because [our] enemies sleep.
There is a good Latin verb for being triumphant: triumphare. It means celebrating victory rather than winning, but I find that appropriate in this context. If you want something closer to winning, please edit the question to add more details. I chose the present tense to make this a general fact. If you want to change to future tense ("we will triumph" instead of "we triumph"), use triumphabimus instead.
A clause like "while the enemies sleep" can be nicely phrased with an absolute ablative. The construction has many possible interpretations as indicated in the translation, but there is no real danger of misinterpreting the message here.
I would personally leave the word nostris out; it is quite clear that if we triumph, then the mentioned enemies are ours. There are couple of different words for an enemy. I went with inimicus, but hostis, adversarius, perduellis, or maybe something else would also work. To see the differences between these words, please consult an online Latin dictionary of your choice.
I understand 'we are triumphant' to mean simply 'we are victorious' or 'we prevail.' Therefore, I'd use vincimus (superamus would also work). Although triumphamus, suggested by Joonas in another answer, would seem the logical choice, this verb most often refers, as Martin Kochanski has pointed out in a comment, to something very specific: the celebration of a triumphal procession, which is awarded (or not) to a general after a decisive victory. This is something quite special and is also quite distinct from the mere occurrence of such a victory.
As I understand it, 'while (our enemy) sleeps' describes just a temporal relationship: during the time that the enemy is asleep, we take advantage of the situation and effect our victory. Therefore, dum dormiunt will work.*
For 'enemy,' there are a couple of options. The best option depends on how/in what context you plan to use the motto.
Finally, I take your motto to refer to a general, timeless truth; therefore, I'd use simple present tense for the verbs vincimus (or superamus) and dormiunt.
So, putting it all together:
dum hostes [or inimici or adversarii] dormiunt vincimus [or superamus].
You could also play with the word order somewhat. Here are two other possibilities:
dum dormiunt hostes vincimus.
vincimus dum hostes dormiunt.
* If you have in mind a more complex relationship, encompassing not only time ('while'), but also causality ('because') or contingency ('if'), Joonas's inimicis dormientibus is an excellent alternative. In that case, though, if you want to use a different word for 'enemy,' you would replace inimicis with hostibus or adversariis.
The implication is that "we" can only win, provided that the enemy, conveniently, falls asleep. Let's depend on luck. In Latin "provided that"/ "if only" is given by dum (or dummodo) plus subjunctive. This may have to go into the future tense, because, presumably, "we" are waiting for the enemy to (conveniently) fall asleep; then, and only then, will we attack. (You may already know that, in Latin, the present tense cannot be used to mean the future, as it can, in English.)
"vicerimus dum hostes (commode) dormiant" = "We shall triumph provided that the enemy (conveniently) sleeps."