Drop in on libraries in your travels. Talk with directors and staff. Encourage your staff or trustees to do the same. Contact international library students - they might return to set up a Sister Library relationship. Look at your community to find natural relationships to build upon - a festival or community specialty that might suggest a relationship with a community in another country.
Many religious institutions have sister congregations.
Find out if your religious institution has a sister congregation and establish a relationship between its community library and yours.