Using a spray bottle is an interesting idea for applying dye to large items.
Dye an outdoor rug.
After a few months of having the rug outside i would not recommend the fluorescent rust oleum paint shown in the middle of the photo below.
I took the rug outside laid it on an old shower curtain dissolved the dye and put it into an empty windex container.
Outdoor spray paint i recommend rust oleum painters touch i used about 3 5 cans for my rug but it will depend on your rug and the design you choose note.
You can keep your color fresh by setting it with a vinegar and salt solution both during and after the dying.
Mine is an ozite 6 x 8 rug in bark it cost 12 bucks and i had a 2 dollar rebate.
Just prior to dyeing add several large potfuls of boiling water which will give your rug a much better color result.
If this size is too big you can cut them down with a scissors to any size or shape you desire probably even puzzle pieces.
I have dyed a lot of clothes but never a rug.
Practice the different colors on a piece of white paper until you are able to match the color of your indoor outdoor carpet.
Stir the dye bath with a wooden stirring stick to evenly spread the dye.
Different carpet dye sticks can be used together to blend into different shades and colors.
Add the amount of liquid or predissolved dye required for your rug.
If you are using a powder dye predissolve the dye in 2 cups of boiling water.
Different fabrics do absorb the dye differently.
Then i sprayed the dye all over the rug until the color was fairly even.
The more synthetic in the fabric the less dye it will absorb.