I still think one shouldn't do that. It gives the wrong impressions to your child that gifting a living creature to someone is acceptable. If your kids really wish for a pet, let them research into the topic, research on your own to and present all the responsibilities that come with owning a pet. If they still want one support them in looking for for one and after finding one take them with you to buy/get it as well as buy the most essential tools for pet ownership. That way they should learn that deciding to own and take care of another living being is a big responsibility while giving them the option to learn for themselves and grow closer to the pet they chose themselves.

After getting a pet let them handle stuff like walking a dog themselves for example (depending on the age) or if they are too young take them with you on walks or a trip to the vet.

I'm not at all a qualified person in any of these fields. I'm a student that studies computer science. My family does have a dog though (which my brother wanted. I'm more of a cat person :D) Those are just some recommendations that feel right to me.