They have tons!

Dogs:

Jasper-Jappy/Jippy, Buster, Baxter(my grandma calls him this), Bud, Goof/Goofball etc.

Piddle-Tiny is the most used, some days that's all I call him. There's also Peedle, Shorty, Diddle, etc.

Wiggles-Wiggy, Wig, Girly, Smiley(underbite), etc.

Cats:

Tigger-Tiggs, Big guy/Big boy, Bully, etc.

Emma-Emmie, Lil' Girl, Miss Prim, Ems, etc.

Lizards:

Ace-Acey is really his only one .

Almond-Alma, Almond Joy, Chubby/Gutty(due to her appetite), etc.

Pecan-Peeka, Peeka-boo, Peek/Peek-Peek, etc.