I have a family friend who is currently struggling with infertility. How do I gently, but still encouragingly, motivate them to keep trying for a baby?

Yes, I agree with City Oh, you don't need to encourage them because for sure, they're doing they're best to be able to conceive a child. Just offer them little help to lessen their stress and workload. For example, watching over their older kids, helping them with some tasks. Avoid giving suggestions like, "Why don't you consider IVF?" You can find out more tips on how to support a friend with infertility here: https://www.verywell.com/how-can-i-support-a-friend-with-infertility-1960033 :)