Tips on Beagle litter box training
The toy breeds of beagle, usually cross breeds with smaller dog breeds, can probably get away with a litter box but you are going to need to be realistic before you employ the litter box solution. Your regular sized beagle is not a good candidate for a litter box. If you are having housebreaking issues with your regular sized beagle then try something else other than a litter box as your full sized beagle dog will choose what option makes them comfortable if you give them an option and you probably will not like their selection.
As was mentioned you will want to limit the beagle litter box training to pocket beagles or beagles that are a cross with smaller breeds like the Chihuahua. Once you train the beagle to use the litter box then be prepared for it to not be an option but rather the dog's choice. A beagle would probably much rather remain in the warm house and use a litter box than go outside into the cold to do what it has to do. But it is a tough go, as a dog is not a cat.
Indoor cats are taught to use the litter box by their mothers and cats have a predisposition to using a litter box. Dogs do not have any of these advantages going for them so it is all on you to teach them how to use the litter box.
Dogs lack this instinct so you are going to have to train them and there are two situations that would require use of a litter box and training in each situation is different.
You may decide that your beagle puppy is going to go through beagle litter box training and never go outside. If this is your decision then get a litter box and get your puppy used to it by placing them in it and offering positive reinforcement while they are in it and when they use it. If you keep an eye on your dog and constantly reinforce the use of the litter box you should be able to train them in a few days.
Some people completely give up on housebreaking their smaller beagle and decide it is a litter box or no more beagle. Put the litter box in the area your beagle has been abusing the most, and then spend the next forty-eight hours placing the dog in the box and reinforcing the positive behavior with strong positive reinforcement.
Put the litter box where the dog does the most damage and spend the next couple of days straight putting the dog in the box every hour and offering positive reinforcement. If all goes well you will have a dog that never leaves the house.