Stop the mess!!!

[WBL]

You could try a coat so they dont' get as wet, or just a fleece, here's a pic of Tiggy in his fleece, they actually shed water pretty good.(don't mind that hat that was for fun)

Next take some treats with you and soon as business is done give lots of praise and a treat. Some basenjis are more stubborn than others. Also I don't know if you go with him, I go with Tiggy when it's bad because he'll just stand and shiver, so we'll both get bundled up and suffer it together, usually he'll go pretty quickly then

[Quercus]

I would put him on a leash, go out with him, and wait until he goes.

[JazzysMom]

@Quercus:

I would put him on a leash, go out with him, and wait until he goes.

That's how we started with Jazz – I was always soaked, but eventually they go.
Once I stopped leashing her, I'd have to step out on the covered porch and play this silly blocking game -- moving from one end of the porch to the other to block her from coming back up until she'd peed. We'd both be wet before she'd finally give up and go.
Now, at almost 3 yrs old, she will go out in the rain w/very little argument, but she does always look back at me from the porch edge and seem to ask, "Do I really have to....?"

It takes time, patience, perseverence, and.... a good raincoat for you!

Keoki has never hesitated unless the rain is really coming down hard.

On occasion, they will both sneak into the covered boat-shed {no more boat} and go poop there in bad weather.

[lvoss]

I walk on leash to potty. When Nicky was young we both ended up pretty wet. It was like he figured if he was going to be miserable we both were going to be miserable. Now I put the leash on and he pretty much races to the first tree.

[elena86]

When it's raining, I watch the Weather Channel to see if there's going to be a break in the clouds anytime soon. If it looks like it's letting up a little, I put on his jacket and tell him "let's go pee pees." I put his leash on and open up the umbrella as I'm opening up the door. Sometimes I have to give his leash a slight yank to get him out the door. The neighbor across the street used to have a big pine tree that he'd pee under when it was raining, but they cut it down this year. Now he just goes to one corner of my yard. Senji doesn't eat or drink at all when it's raining. Sometimes he'll drink a little water right before I take him outside. Mostly, he gets catatonic and just spends the whole day sleeping under a blanket on the sofa.

[sharronhurlbut]

We use rain jackets on the dogs, and most of the time it works.
However, when the rain is blowing sideways, I have to put them in the car and take them down to the park, about 3 blocks away.
I don't know if its the excitement of the car, the new doggie smells in the park.
But we always have "action" down there.
I do know some folks have litterbox trained their dogs, or put a bunch of puppy pee pads in the garage, with a doggie door for the dog to us.

[youngandtired]

I trained Sahara to go outside for business on a leash, so when it is raining I put her leash on and grab the umbrella. At first I would have to yank on the leash to get out of the door and down the steps, now she goes as long as I go with her, and the umbrella goes as well. Now she pretty much goes by herself when it is just drizzle, but with hard rain, she will hold it till I have to go with her. When we get back in, I praise, praise and praise with treat in hand, I say, "Sahara, Good Girl go potty outside," she seems to know what I am saying, just keep this up and they will learn they have to go out in the rain eventually. Sahara has learned the quicker she goes in the rain the faster she gets out of the rain, these dogs are smarter than the average dog. Praise, and treat, Praise and treat, it really does work.

[wizard]

It took a lot of patience and getting soaked when I first acquired EL D but it helped that I have a deck and trees he could go under. Pooping was a different story because he would wait about 30-45 minutes after peeing and at first wouldn't go unless I took him on a walk which didn't work no way no how in the rain. I finally worked with bribery and lots of praise whenever he would do his business and it's not nearly as much of a big hassle. Hang in there.

[Barklessdog]

I would put him on a leash, go out with him, and wait until he goes.

Our dogs never will go out unless you do the above, then they are fine unless it's a huge down pour. Rain seems to bother them little if you go too.

[torchsong]

She-Ra's no fan of the rain, that's for sure. We use pee-pads and these past few days we've gone through quite a few (had a pretty rainy spell), but if we go out with her she's usually okay.