Show these pictures when someone says they are having a baby and they need to get rid of their pets...
That excuse strikes a raw nerve with me and it's even worse when the person is going on and on about what a wonderful pet it is and how hard it is to give them up. If the pet is that wonderful and dear, then it shouldn't be too hard to make the adjustments necessary to keep the pet. It is hard to find homes for senior cats and dogs and it's a difficult adjustment for an animal that probably has been raised from a kitten or a puppy with that person.
People need to make a real commitment when they adopt a pet, for the lifetime of that pet. It shouldn't be so hard to keep a pet and infant separate if that is your choice, but it would be better to deal with the two together -- better for the animal, of course, but also better for the child to learn about animals from a young age.
If you can't deal with the pet and the child, it is the your responsibility to find a good new home and it may take some time. Dropping it off at a humane society where older animals (and I mean older than a year or two) are routinely euthanized without ever being put up for adoption at all is unconscionable.