As suggested by 
hobbit_dave or possibly Hugo WINOLJ at our open house: stillsuits for infants. It's not that you necessarily want or need to recycle the material that exudes from every orifice, but that having a single tap for drainage would be very useful.
Also, forget Zero Point Energy as an SFnal power source. We really need to be harnessing all that waah-ing and all those flailing limbs.
Haven't had to change my nephew yet - well, just for damp nappies, which is fairly clean to do - but I've seen him flail around enough to get stuff everywhere. And manage to pee on his mother three times in one day...
As my now-dead grandmother would have said: that'll learn 'im.
As little **FIXME gets more vigorous in his habits, I've been thinking about some sort of repressor field/flotation tank for sleeping. The baby would be free to rotate and flail freely in 3D to wherever they were most comfortable, with no risk of getting their leg caught in cot bars, or lying uncomfortably on an arm, or ending up with their nose squashed painfully in to the matress.
Slightly less flippantly, I intend to build a hefty vibrating dingus that I can strap to his baby bouncer and tune to its resonant frequency (I've taught myself to bounce it with my toes, but it's still a bit awkward).
You do know that you can buy baby bouncer/chair/whatever type things with a vibrating thingummy built in? Not cheap new, but very reasonable second hand, and if you're anything like me you've probably a lot less time for fun little projects like building your own electric gizmo these days. (If I'm honest the time it'd take me to get round to it is probably about the same as the time it'd be useful for.)