I am meeting a friend tommorrow after three or four years. Last time we met, her son had not been born and her father had not died. It would be churlish in my opinion not to acknowledge either event, but it seems…weird attempting to congratulate and commiserate in the same breath. How would you go about it? Separate the two? Congratulate first and commiserate 10 minutes later? Avoid totally (my preferred option, but not really realistic.)
" Your life has been very eventful since I saw you last. How are you doing?"
Makes it sound like she has been travelling overseas or started a new job. Thanks though for the suggestion. 
Practically anything works said with the right emotion behind it. How about “I know a lot has happened. Tell me about your son.” Then after that topic is exhausted, switch to parent’s death.
Honestly, after a year, I probably don’t want to spend my whole time talking about how someone I knew died. In fact, I probably don’t even track who knew about it and who didn’t. So I’d say, probably get in “congratulations on your son” and “so sorry to hear about your father” in the first twenty minutes, but don’t dwell on the death unless she wants to talk about it. The son seems a reasonable opening.
everything depends on timing-when did the death and birth happen? I guess I would tend to first acknowledge whatever happened most recently…
But really, just be open and ask her how she is doing, which is perfectly neutral and appropriate. Then take this as a queue to offer sympathies or congrats or whatever. It would seem to me to be a little forced and awkward for you to offer this right away, just go with the flow. You might talk about you for the first few minutes then transition to her…
About a year ago, IIRC her father died (quite suddenly) when she was expecting.
Go with a simple “How are you?” or “How have you been?”, and let her tell you what she wants to share.
I have to say, I’m in exactly this position (my father died unexpectedly in October and my son is due in July), and I think it’s pretty good. It lets her focus as much or as little as she wants on either topic, or how she feels overall. And depending on the day you catch her, she may be focused more on her son or on missing her father.
As a widow, I can speak from personal experience and with some authority on this subject.
I can tell you that when I meet someone I haven’t seen since before my husband’s death, I HATE that they feel they have to tippy-toe around the subject and not mention him. To simply say, “How are you?” without acknowledging what we both know has gone on is… well, it’s frankly chicken and creates awkwardness where there doesn’t need to be any.
People sometimes think that bringing up my husband’s death will “remind” me, but in fact, hardly a moment goes by when he’s not on my mind, and this was true even several years after his death. He lived. He was a real person. He meant something to me. So if you run into me, I WANT you to say, “I was so sorry to hear about Bob’s death. How have you been doing?” Don’t be afraid to bring it up! You’ll be doing ME a favor by not making ME find out if you already know. It’s not a taboo subject.
In the case mentioned in the OP, something like, “I heard that your dad passed away and then you had your lovely son. That must have been a difficult time for you, such a mixture of happiness and grief. How are you doing now? And how is the baby? Tell me about him.”
You don’t have to protect me from the events in my own life. I lived them. And YOU are permitted to talk about them… you won’t be reminding me of anything I’m not constantly thinking of anyway. Show your feelings. Reach out. Put your heart on your sleeve and reveal that you care, and you’re hurting for me, and you want to know how I am. God, I was so grateful for the few people who sincerely asked me what was going on with me. But most people didn’t know what to say, so they skirted the issue and acted like my husband never existed. Even people who knew him well did this. It hurts when that happens.
In all honesty, before I lost someone dear to me, I was one of the people who avoided the topic. I thought I was doing the grieving person a favor by not bringing It up. Now I know better. If you care, act like it, talk like it, and show it. You won’t be making a mistake.
Sometimes stating the obvious is the best way to start. But since we don’t really know what the other person is thinking/feeling we can start with ourselves.
After the usual small talk and if it doesn’t make you feel too vulnerable the statement, “This feels a little awkward to me and I’m unsure how to begin.” opens the door to letting the person guide you.
If the other person has any hurt or animosity about your absence this may soften it and open the door to an intimate conversation.
I’ll admit that it’s a risk to state our feelings (without acting them out) in potentially difficult situations but with a little practice I’ve found that it has surprising results.
This.
ThelmaLou gives good advice here in my opinion. This way she can talk or not talk about what she wants. Good Luck!
I agree - that acknowledges and opens up the subject of both.