Glue is usually toxic to pets and humans, because of these harmful ingredients in it:
- Light aliphatic naphtha
Because of this, it was hard to find a non-toxic option. I did find one brand, but I would still be extra careful with it and immediately call a veterinarian if your dog digests the glue or starts to act weird after being in contact with it.
According to trendhunter.com, Eco-Bond's glue is pet safe.
The source claims that Eco-Bond is completely non-toxic and safe for children and pets.
I didn't find too many of their non-toxic choices on Amazon (I did find this currently unavailable option on Amazon though), but Eco-Bond does have a website where they display around six non-toxic glue choices to choose from: https://www.ecobondstore.com/.
Assuming that this is legit, the glue would work on your dog's toy.
However, the glue won't last forever (and you wouldn't want your dog swallowing parts of the toy if it did come apart again) and even this non-toxic choice isn't the best for pets, so I would consider buying a different toy.