I have heard that birds need to eliminate every 10 to 20 minutes. I have also heard some birds can be trained to poop on command. We are considering a pet bird in the house, and are wondering which types of pet birds can be house-trained?
The parrot family appears to be quite trainable, likely a function of being highly intelligent. However, any bird species that you're likely to allow to fly freely can be trained with appropriate patience. Several articles out there also describe the basics of it:
Essentially, the idea is to watch for signs that your bird is about to poop and then move them to an appropriate poop spot and then tell them to go. Reward them when they do it correctly.
Having said all that, this training is not without some risks. Birds only have one sphincter and they urinate and defecate from that one opening, so this is a biological structure that is not intended for long-term "holding it in" activities. The single biggest risk here is the prolapsed cloaca which poses serious danger to the health of the bird.
At any rate, I had a pet budgie once and allowed him to fly freely around my apartment at the time. The thing is, he tended to hang out at two general places: some rings I'd set in front of the balcony and in the cage I had hung on the wall. If you know that birds tend to poop when they take off before flying and for a while after eating, appropriate paper/plastic cover at their hangouts is a good way to avoid any significant cleaning chores.
Summation: pick the variety that appeals to you the most. The parrot family is good if you like to talk with them and budgies (it is a small variety of parrot), in particular, are really, really, easy to keep.
There are other ways to deal with poop than potty training.
As John said, potty training is not without its risks.
What we do instead:
Put paper under the bird's favourite places (under the cage, a few spots in the room).
Have a shirt or a short cape specifically for this purpose, so the bird can stay on one's shoulder or knee without soiling good clothes.
After a while you'll learn to tell when the bird is about to poop and you can catch it, hopefully with a piece of napkin ... I got pretty good at this over time.
The consistency (and cleanability) of the poop depends on what the bird ate and especially on how much it drank. Drinking warm water (or drinking a lot during a bath) inevitably leads to a mess. You can be prepared, or just put it in the cage for a while after drinking a lot.
That said, birds can be quite messy and accidents will happen many times.
Regarding the intervals, for cockatiels it's about 10-20 minutes, as you said. I believe for bigger birds it's longer.