How do I deal with dogs that won't stop barking?

Personally, I would let the owners know I'm not the best fit for them. If you're determined to keep them as a client, you could try earplugs or ask the owner what methods they're comfortable with you using to train them.

It really depends on why they are barking. It sounds like they are on high alert because their owners aren't home and are barking at "potential threats": car going by, sound they heard, squirrel, etc.

Start off with closing all the blinds so that they can't see cars passing by, squirrels, etc. Keep the TV or radio throughout the day/night to minimize the random sounds that they may hear and be barking at.

Distract them when they are barking. If they're outside barking, bring them inside to play or for treats.

Finally, ask the owner if there's anything that they do to prevent the barking. Some people use an ultrasonic bark deterrent, though some dogs are super sensitive to them and will go and hide. See what the owner wants you to do.

Some of my dogs tend to be on high alert the first day when my husband travels out of town. So it could be just the first day or two while they get used to you being the one there.