You can offer a free ad in your newsletter to a pet store in exchange for a donation. Ask each member to contact their local pet store and initiate a conversation with the owner, asking to place a poster or set business cards on the counter. It never hurts to ask. You won't always be successful, but at least you tried. You just have to take the first step and ask.
Some people are more aggressive than others.
If you're the shy type, then maybe you can help your club in other ways. Many catalog companies will ask for membership lists in return for giving discounts, but be careful. There is a confidentiality issue involved here. You can have a form available which members can sign. Some individuals might want to be made part of a mailing list, to have the newest products made available to them, while others might think of catalogs as junk mail.