Set up your design in Able Sisters and replace everything else with umbrellas and hats and other design types that villagers cannot wear. Then just wait for them to change out of their normal clothes for the designs at Able Sisters.
If you just want them to wear your designs in general I think it'll just happen, fill up your Able Sisters shelf and wait. Almost all of mine are wearing something off there now (not always an appropriate one though).
Specific designs... no clue. Even if you got them wearing preferred ones, they'd start swapping them around when your back's turned, so it might not be possible. One of my designs I took down weeks ago and yet it's still spread from Egbert (the single initial wearer) across half the village population.
You could make a design, and make it the only one that's a shirt on the mannequin.. Then once they've changed, change that one into an umbrella
Then you could do the same for another villager..
But this process could take ages, and there's no way to influence when they'll change into a design.. Could take days, could take months.. Plus other villagers may change too
So unfortunately, if you wanna influence, you gotta send them clothes through the mail (which doesn't always guarantee them to wear it), or just only have one pattern they can change into
I've noticed that TT helps. I've been trying to get a villager out for almost a week (real-time), and most of my villagers have changed into my winter sweater design. I set all of my mannequins to that specific design though.
I've sent villagers clothes, but they don't usually wear them. A couple of days ago, I was trying to boost my letter writing and I had an inventory full of stuff I was holding to sell to Re-Tail the next day. I decided to randomly attach the stuff to the letters. The next day, I saw Gala walking around in the flight-crew shirt I had randomly sent her. I need to take a screenshot because she really looks adorable in it.
Meanwhile, Kabuki has been wearing the bubble-gum tee for about a month and he still tells me he's just trying it out but the tag is itching him.