I tend to NAir and Fair more during desynch combos.
Nair usually sets up for a dash-attack which, if you aren't feeling the combo, is good for setting up Uair juggles. It's definitely good for the floaty characters who we can't combo that well(Samus, Peach, etc).
Fair has really good stun time, both on you opponent and with non-l-canceling lag so it allows more follow-ups for the free twin without breaking the desynch. It also, for the most part keeps them in one place because the Fair has almost no horizontal knockback. It's up to you what to follow up with. I usually tend to follow-up with another Fair, or a WDUsmash. On Fast-fallers, this can lead into a Fairspike which will lead into a sexy tech chase.
I can see where Dair may be useful though. Fairspikes send an opponent down if you knock them up. Usually into a tech-chase or a finisher. However, it is difficult (at least for me)to get the fairspike when I'm in the middle of a combo, trying to control both Nana and Popo. Dair doesn't reverse the momentum but it does completely halt it, Allowing different follow-ups(no tech-chase but juggle potential, I guess) but at the cost of stun time (for the opponent). It's good to change things up.
I went through this period where during Desynch combos, I'd constantly try to get nana to either toss a block or blizzard the opponent. Once I grew past that point and started using things like Ftilts, Nairs, Dtilts, Fairs, and Dash attacks, I felt my game step up immediately. I think I'm going to finish that desynch guide and post it.
Here's something cool. I pivotted a jab and had Nana dash attack the enemy. I then fairspiked them to the ground and fastfell. Nana happened to be where they were and jabbed them, making them stand up, giving me the grab! LOLz. Desynched Thunder's Combo FTW.