Flourish Online, in a series about churches being part of the community, suggests helping the local animal shelter through adoption and other assistance:
...while a mass congregational adoption might not be the best idea, there is still plenty your church can do to advance awareness about the need for animal adoptions and save the lives of thousands of God’s precious creatures:
Healthy animals land in animal shelters for a variety of reasons; they are not cast-off because of their health or behavior, and they require no less care and attention than the most pampered pet in the best of homes. Volunteering at a local animal shelter provides animals with the attention they need and shelter staff with extra assistance, but it is good to communicate with your local shelter to determine just what their needs are and how members from your church might help.
Spread the news at church: The Humane Society of the United States will eagerly supply churches with materials that can be included in church bulletins or handed out after service to raise awareness about adoption needs. Such resources include statistics and stories that will inform church members about the true needs of shelter animals, and encourage them to consider adoption in light of our call to care and compassion. There are also resources available for educating children about taking care of animals in a responsible way.
Spread the news outside of church: Animal shelters often hold adoption days in pet store parking lots or on community center grounds, but they can also bring pets in need of a home right to your church. Consider hosting a pet adoption event as a way to educate your church community on pet adoption and simultaneously invite the larger community into your church’s space to experience God’s care and concern for these creatures. An animal shelter will bring animals and materials to you, and folks from within and outside of your church can meet the animals while you greet them and provide them with information to battle the stigma shelter animals so unjustly receive.