Okay, this is what you NEED TO DO if you cannot locate a vet immediately. It may buy your guy some time.
Gather the goat, a helper or even two, a sharp pair of scissors dipped in antiseptic, a thin strip of gauze and a small jar.
Flip the guy over and sit him on his rump, with his belly exposed. Have someone hold him in that position (the holder can sit in a chair and prop the goat's back against their legs, holding the head and front legs to keep him immobilised. Sometimes a blanket over their eyes can help keep them quiet.
Locate his pizzle (where he pees from) and locate the area where his scrotum would be if he was intact. Feel around between the two spots and you should feel his penis - in a little guy it will be quite small, the thickness of your little finger (or smaller if he's a mini).
Now, take one of your hands, feel down along the penis to the area where his scrotum would be, grasp the penis in your hand, push into his belly and then upwards towards the pizzle. You may need to slide your hand slowly upwards towards the pizzle also. At the same time, place your fingers on either side of the pizzle and draw the skin down towards the place where his scrotum would be. What you are aiming to do is for the penis to pop out from the pizzle. It can be tricky especially on a castrate, and especially on one so young, so it may take you a bit of fiddling, dont expect to get it on the first go (I rarely get it on the first go with little castrates, and I've done it plenty of times).
Basically what you are trying to acheive here is to straighten out the sigmoid flexure to lengthen the penis and allow it to come out of the pizzle. This picture might help you visualise what you are trying to do - the sigmoid flexure is the s-shaped bend.
When you get the penis exposed, get a helper to wrap the gauze around the penis and hold onto it, that should leave you free to let go of his penis that you are holding through his skin. Now, at the very tip of his penis there is a fine little hair type thing, called the urethral process, shown here in this pic:
Take the sharp pair of scissors and cut it off. In the majority of cases this is where the stone is lodged. Put the urethral process in the jar, along with any stones you might find (you can sometimes see them and pluck them from the penis if they are large) for the vet to analyse.
Now, sometimes the stone is further back, in that sigmoid flexure, and this procedure will not help in those cases but it is a good first step to take, we routinely do it on all animals if UC is suspected.
He still need to go to the vet; vets have after hours emergency numbers for weekends and night emergencies, and that is what this is - an emergency! If they say they dont deal with goats, ask if they deal with sheep - UC is common in rams and wethers in sheep as well. And if they say they have never done it before in goats, tell them that you understand their concerns, and all you ask is that they please have a go at it. My vets (Stacey and Mark) are not very experienced in goats but are always keen to have a go and do their best with my goats.
If the stone is not in the urethral process, ask the vet about doing a perineal urethrostomy; this is a pricey surgery but if he is a pet you may not be too worried about the money. Basically they open the penis above that sigmoid flexure so that the wether starts peeing out his back end like a doe. This is probably the only real treatment for stones in the sigmoid flexure; there are drugs that they try to give them to break down the stones but in my experience they cost a lot of money and dont work anyway.
