I also have cats – three, to be exact. Took them into the house from the streets of Jerusalem when they were small, weak and sick. Now they’re the happiest and healthiest cats in the world. In Israel, especially in Jerusalem, there are hundreds of thousands of homeless cats.
Now, this may sound a bit funny – but indeed, I was wondering whether there was somewhere, anywhere, I could mention my cats now and then in prayers. What I do now is that I mention them in birkas hamazon (grace after meals), since one can pretty easily add all kinds of people there. (there is a section that goes like “may the Merciful one bless my wife/husband, my father, my mother, my children…” as applicable; I just mention “my wife, my father, my mother, and my cats”). I realize others may think it’s a bit weird, but I can’t see anything wrong with it.