Ok! Well, here's a possible solution if you can't find an inexpensive sprayer.
1-Purchase a large bottle of weed killer with the water hose sprayer attachment.
2-Empty the contents into a container to be reused later.
3-Purchase the amount of bleach required and fill into weed killer bottle.
4-Attach water hose.
5-Spray as needed, refilling with bleach as needed.
6-Only problem; Is this a correct mixture? It will get the bleach down!
7-It will also leave you more money to pay for your dog/s!
You will also have to clean up thoroughly inside your house!