I'm not strictly UP but I do follow lots of the principles.
I try to work on cultivating habits. If I ask 2.1 y.o. DS to do something and he doesn't do it, I immediately 'help' him to do it and try not to ask him a second time so that he learns to listen to me the first time.
If he does do as I ask, I say 'thank you for doing as I asked'. If he's cross, I say 'thank you for doing as I asked, especially since you didn't want to do it' and I might give him a kiss.
If he is cross and saying 'no' to something, I try to understand what it is he's cross about. e.g. 'are you saying you don't want your shoes on because you want to wear wellies instead, or because you wanted to stay here and play with your trains?' Then I will either change my mind about what I'm asking (if I can easily) or acknowledge his feelings and reassert what I want him to do, with an explanation. e.g. 'I can see that you'd like to stay and play with your trains. It would be lovely if we could, but if we don't go out to the shops we won't have any clementines to eat. Let's put your shoes on'
We do natural consequences too, e.g. refusal to put a toy down means I take it away and put it down for him. If I do have to do something like that, I explain that I don't like having to 'discipline' him but that I want him to learn x.
We have certain rules e.g. when playing at the sink, if the water goes all over the floor, that's the end of playing at the sink. The consequence isn't a punishment, but an action-consequence link.
I do offer incentives but not bribes. So I wouldn't say 'I'll sing you a song if you lie down for a nappy change' but I would say 'I can see you don't want to lie down for a nappy change. Would it help if I sang you a song?'
Other incentives might be choices. So if DS doesn't want his shoes putting on, I might say 'would you like your right shoe on first or your left one first?' It makes it clear to him that what I said will happen, but still gives him a sense of influence over what is happening to him.
I'm more inclined to take a gentle 'just make him do it' approach to things like seat belts, hand washing, eczema cream / medicine, sunhat wearing etc than to offer rewards. When doing so, I would usually make sure I'm modelling doing it myself, talk about how/why we all have to do it, acknowledge DS's feelings about the matter and give him choices where I can, even if they're just made up ones like 'would you like to hold your tractor or your car while I put your seat belt on'.
On trying new foods, I am 'training' DS to be a less fussy eater by giving him one food he doesn't like as the first bite of dinner every day for 7-10 days. I say something like 'I'd like you to try this please. You don't have to eat it. You can spit it out if you want to, but I'd like you to put it in your mouth and try it please.' I'll then say thank you for trying it. He's been willing to do that much, and has got to the point of asking to have both foods I've tried it with so far. Having the habit of doing it every dinnertime helps, as it's just part of the routine now.
On pottying, I read a book to him on the potty by way of an incentive and on the toilet he only gets to use a piece of loo roll to wipe with if he's tried to do a wee (because he doens't need wiping if he's not done one). So again, incentives rather than rewards. But I'm a SAHM and he's not going to nursery so we're in no rush.
I'm not averse in principle to some more mainstream approaches to discipline/punishment but they would be a last resort. DS is a naturally compliant and sensitive child so I've not had to go down this route (yet!).