I’m in a similar position at 36 and tbh everyday is hard and it feels like my chances are slipping away...especially in a lockdown where I can’t meet anyone.
Next time she sighs or makes the comments, use that as an opportunity to deepen the conversation. It now helps being able to speak to my parents but that’s only since I needed their support to stop me ending my own life before Christmas because of being unmarried and childless. Before that I couldn’t talk to them about it.
My suggestion would be picking up on her expressions, comments etc “DD you looked really sad when we bumped into school friend. What’s on your mind? Can we talk about it, I’d like to help.”
Or
“I know you’ve always loved children. I sometimes worry that it might upset you that it’s not on the horizon for you just now. If you’d ever like to talk about it, we can.”
Or when she let out that comment about her cousin, sympathetically,
“Oh that was a big sigh! You sound down...are all these pregnancies getting to you? I think I’d feel that way too.”
With me, my main problem was that I was rejected by all the men in my life growing up (Dad, brothers, uncles, no grandads) and then terribly bullied at school so although I am very attracted to men, I’ve just never thought anyone would want me and I felt quite unlovable. I’ve not been asked out on many dates, none at all until I was nearly 30.
So it might help to try and find out what the barriers are for her. Is it confidence? Is she just not interested in relationships? Does she wait to be asked out and isn’t getting asked out?
If she wants a relationship, helping her see her wonderful qualities would help her self esteem and fully encouraging her to meet people. Either online or through hobbies when they restart again.
Please also don’t treat her like she’s infertile! It’s a different issue and will only fuel her anxieties. She’s easily young enough to meet someone, marry and have children. She just might need to get very proactive if it’s definitely what she wants.