How to Say Congratulations Without Looking like a Stalker?

Knock on their door with a plate of cookies or basket of muffins and 2 coffees, one decalf for the Mom. Simply say "Hi, I just wanted to officially introduce myself and say congrats on the baby". Ask to see the baby's room and just get to know her. Ask if she needs anything and let her know you are available to help. As you know the first couple of weeks with a new baby are difficult, no sleep and horomones raging does not make a pretty package.

I had a similar situation - there was a neighbor a few houses down who had kids about my kids' age and I wanted to get to know them. I don't have the personality to just knock on strangers doors, so I asked my outgoing aunt how she would approach these folks. She said "bake cookies with your phone number and bring them over." This is not my style or personality, but off I go. They weren't home so I left them on the stoop. The woman never called, then after a while (like the next year) I ran into her at a garage sale and it was so awkward. Fast forward another year or so and of course her daughter was in my daughters kindergarten class and we saw each other every day dropping off and picking up (we live close enough to walk to school). We became acquainted and friendly only because ignoring each other would be rude. I felt awkward around her and she never took to me either. Whatever you do, keep it casual, even if it's planned casual - like you see her outside and decide to take a walk at that moment :) I learned a big lesson from this.

Make sure she is pregnant first. I worked in retail for a long time- never make any assumptions about anyone unless you know for sure. Certain medical conditions can give pregnant looking symptoms. You don't want to be left with egg all over your face.
Once you are sure, send a card in the mail. If you want to go a step further, wait until the baby is born and take them dinner one night. That, to me, was the most thoughtful thing my neighbors did.

I wouldn't do anything until you run into them and they bring it up. Because you aren't close, you can't be sure of the situation. Take the dog for a walk if you see them out in the yard, stop by and be neighborly. If she is pregnant then you can offer your congrats and get them a little something if that's what you would like to do.

I like that note on the door deal. That is sooo nice and should win you friends for life!

If you feel uncomfortable about knocking on the door, write a nice congratulatory note and stick it in the door. You could mention that you're the lady with the dog who lives at the bottom of the hill, you'd like to help if she needs anything, and that you'd like to get to know her better. Let her know your phone number, and let her take it from there.

I would snail mail her a 'Wishing you Well' card.

We have a pretty tight neighborhood, but those relationships began with a simple "Hi, how are you?".

Just a thought... next time you see them outside- find a reason to take a walk... the dog? Stop and ask her how she is doing and how she is feeling. Clearly she's preggers, so no risk of offending. Chat her up about whether it's a boy or girl... when is she due... call if they need anything, etc.

When the baby arrives, bring over a casserole and a box of diapers. Our neighbors have been doing that for the last couple of weeks... we have tons of "stuff" for the baby (due in 3 weeks), but who would turn down a casserole and some diapers??