You suggested in the second sentence of your answer to the related question, which spawned this question, that you're using 'conveniently' to talk about a lucky break, so that it really means something like 'if we're lucky,' 'as luck would have it,' or 'if things go our way.' Unfortunately, although English 'conveniently' may be able to be used like this, Latin commode can't, and this isn't what, e.g., Oxford Latin dictionary means when it gives 'conveniently' as one of the definitions (as examination of the various attestations that are provided will make clear).
However, there are other ways of talking about things that come to one as a result of luck or good fortune. In a comment, Tom Cotton suggested adverbs such as forte, and there's also the ablative noun casu – in fact, the two Plinys use both of these together: forte casuque. Another way is to use the verb contingere. Here are two examples:
Seneca the younger, Epistulae morales ad Lucilium 30.12:
iam vero si cui contigit ut illum senectus leviter emitteret, non repente avulsum vitae sed minutatim subductum, o ne ille agere gratias diis omnibus debet quod satiatus ad requiem homini necessariam, lasso gratam perductus est.
'But if it falls to anyone's lot/good fortune that old age releases him gently, not suddenly torn from life but gradually removed, truly that man ought to thank all the gods because, after getting his fill, he has been led to the rest that's necessary for a human, welcome to one who's worn out.'
Livy, Ab urbe condita 28.41.4:
nisi aut Hamilcar Hannibali dux est praeferendus aut illud bellum huic, aut uictoria illa maior clariorque quam haec – modo contingat ut te consule uincamus – futura est?
'Unless Hamilcar is to be rated more highly as a general than Hannibal or that war more highly than this one, or unless that victory was more significant and more famous than this one is destined to be (provided that we're lucky/fortunate enough to win while you're consul)?'
Such a use of contingere would give this:
vincemus dum (nobis) contingat ut hostes dormiant.
'We shall triumph, provided that it is falls to our lot/good fortune that our enemies are sleeping'/'...provided that we're lucky/fortunate enough for our enemies to be sleeping.'
(Note: I don't think the future perfect that you've used is required – or even desirable; so I'm using a simple future instead.)
There's also the related verb obtingere, which can be used in a similar way; but since it's quite often used in situations that involve drawing lots for something, it may convey a somewhat stronger sense that luck is involved. Therefore, you can replace contingat with obtingat.
Of course, the notion of the enemies' own complicity, which you've said you're also interested in, isn't particularly strong here (it's merely an implication). To highlight that notion, one possibility is something like this:
vincemus dum hostes dormientes/per somnum [or even dormiendo] (se) in exitium ruant.
'We shall triumph provided that our enemies, as they sleep [or 'by sleeping'], plunge/cause themselves to fall/rush blindly into destruction.'
Although the verb ruere can be used either reflexively or non-reflexively (intransitively), and the meaning is similar, the reflexive may be desirable here to underscore the fact that the disaster is something that the enemies are bringing on themselves.
Here are some example of this use of (se) ruere:
Aulus Gellius, Noctes atticae 7.2.8:
sin uero sunt aspera et inscita et rudia nullisque artium bonarum adminiculis fulta, etiamsi paruo siue nullo fatalis incommodi conflictu urgeantur, sua tamen scaeuitate et uoluntario impetu in assidua delicta et in errores se ruunt.
But if they are rough, ignorant, crude, and without any support from education, through their own perversity and voluntary impulse they plunge into continual faults and sin, even though the assault of some inconvenience due to fate be slight or non-existent. [Trans. J.C. Rolfe]
Tacitus, Historiae 1.84 (Otho speaking):
si Vitellio et satellitibus eius eligendi facultas detur, quem nobis animum, quas mentis imprecentur, quid aliud quam seditionem et discordiam optabunt? ne miles centurioni, ne centurio tribuno obsequatur, ut confusi pedites equitesque in exitium ruamus.
'If Vitellius and his gang could put upon us any sort of spell they chose, surely the very attitude of mind they would pray for would be mutiny and dissension, that the private should disobey his centurion and the centurion his tribune, that in an inextricable chaos of infantry and cavalry we should rush blindy to our destruction.' [Trans. Kenneth Wellesley]
If you really want to bring out the notions of both 'convenience' (luck) and complicity, I suppose you could combine the 2 approaches by using both contingere/obtingere and se ruere – for example:
vincemus dum contingat ut hostes dormiendo se in exitium ruant.
Still, this seems like overkill to me. In fact, I think the very best translation is, as it so often is, the simplest: just vincemus dum hostes dormiant, 'We shall triumph provided that our enemies are sleeping.' (Tom Cotton's answer also deserves serious consideration.) It's clear enough that the enemies' being asleep would be a convenient stroke of luck for us, since it would, against all usual expectations, fulfill the condition (proviso) that allows us to be victorious. It's also likely to be perfectly clear that the enemies would have only themselves to blame for defeat (that is, they would be 'cooperating' in it) if they all fell asleep without at least posting a couple of men to keep watch.