How can I make a weed killer that will not harm my animals?

The only thing I can think of is pouring boiling water directly onto the weeds.

Vinegar or boiling water won't leave anything harmful to pets.

Use a 1:1 mixture of white vinegar and water and spray using an empty spray bottle. Boiling water also works.

2 cups white vinegar

¼ cup salt

Squirt of dawn

Mix in a spray bottle. If you have a larger area, you can mix in a garden sprayer with larger quantities. Use when it will not be raining for a few hours so that it isn’t washed away.

boiliong water or straight vinegar pour onto plant soaking down into center roots

White vinegar in a pump sprayer is all I use. If done on a hot sunny day, you can literally watch the weeds perish.