"My son is 2 years old and has been showing signs of potty training readiness for months. He sits on the potty often and always uses it to poop but he will not pee there. Instead, he holds it in, brings me a diaper and begs to pee in it. We take him to the potty, which is by the couch in the living room and have him sit down. Then he just sits there crying and wants to pee in the diaper. Sometimes I put him in cloth training pants and he will go in those, too, but not in the potty. He's been to the doctor so we know there's no infection or pain. We don't know what to do."
It's good to hear that you've been to the doctor and have ruled out any medical issues. When a toddler is having problems urinating but is pooping on the potty without problem, seeing a health care provider is my first advice to rule out any type of infection or problems with the penis like meatal stenosis. It's also good to know that he's going perfectly well in his underwear or a diaper with no pain. That's great and show's that he's capable of urinating when he wants to do so. What I wonder about are two things: First, that he may want more privacy than a potty next to the couch can give him and second, that he may not want to sit to go pee.
To remedy these issues, try moving the potty to another location (like the bathroom) and be sure to give him some space and time alone. Whichever spot you choose, make sure it's child proofed so he's safe and doesn't get into any mischief. Then, instead of instructing him to sit down to go, encourage him to try standing up. I suspect he may not like the way it splashes back or he may not feel like he's able to control the stream yet when he's sitting. He may resist letting it out because he's afraid it's not going to go into the toilet. If, on the other hand, he insists (on his own) that sitting down is the way to go, try choosing a potty chair that has a splash guard.
You might have some difficulty at first since he's already resisted peeing on the potty and it's been a situation fraught with tears and stress. It might be tempting to just give him the diaper and let him do his business in it. I might even suggest that if I didn't already know that he goes poop in the potty without any issue (congratulations, because it's usually poop that is the potty training problem) and that he's not resistant to wearing cloth training pants. Instead, I'm going to advise you to get rid of the diapers completely and only put him in cloth training pants.
If he is still upset, let him know that the potty is the place to go pee just like it's the place to go poop which he already does so well. Remain calm throughout, gently lead him to the potty and give him some privacy. If he wants to go in his training pants, then he's free to do that, but let him know he needs to be in the bathroom, standing next to or sitting on the potty. Also let him know that he will need to clean up and get changed into new, clean training pants. Then, if he pees, don't be upset, but help him go through the steps of cleaning up and keep verbally reinforcing that the potty is the place for pee. I don't think it will take long after for him to feel more comfortable and start going pee in the potty.
Definitely don't pressure him too much or express too much outward disappointment with him or he's likely to keep on withholding it. Part of being able to urinate is being able to relax and let it flow, so you don't want him to be worked up. He will be unable to relax if he feels like there's a lot of pressure on him to go or if he thinks that you are upset or worked up over the situation. And rest assured that your son will experience more success at potty training in time. You're halfway there already.