I’m unsure if any kind of penguins can lay the Golden Egg but I used Brows Penguins. One is a Crimson Brows Penguin at level 27 and the other is a Purple Brows Penguin at level 34.
Incidentally, I highly recommend NOT giving love to any sort of eggs at a neighbour’s farm since there are animals that give much higher XP. For example, the Spring Flower Deer gives 87 XP.
koukoupuffs 
You helped me sooo much with the Halloween posts for tiny farm and when I saw you started the golden egg I got psyched up! 🙂 I have only gotten one golden egg from breeding a red and a normal penguin. I got two brows but ones normal and ones purple, do you think the odds are better the higher the penguin? Add me if u got room, I play everyday and I know a secrecy way to get 1 or 2 extra bells a day.. But I don’t want to post it cause I don’t want them to fix it. My screen name is: Ashofember
I have no idea what the odds are for any penguin type. 😦 The Brows ones were the only one where I had 2 of already. I didn’t want to spend time waiting to raise other types. ^^; I’m having a heck of a time now getting Golden Eggs with my Brows penguins though.
Bred them around 3 times already today and didn’t get a single GE. I’m on the third objective (where it says to breed 7 more GE to get the goofy looking Cinco de Mayo chick).
……….. Is it even possible to max out on friends? I do have more than 15 so I don’t visit everyone every day. I do plan on ditching ones that don’t seem to ever visit or tend to their own farms though.