I think I have an answer. This has been one of the most frequently asked and theorized questions in regards to the Super Mario Bros. franchise, and here I'm going to toss my hat into the theoretical mix. However, I'm going to use actual game-only material to back my shit up, unlike everyone else out there inventing Koopa Queens to fill in the missing pieces. So put on your plumber caps, because we're about to take a journey down Pipe Maze Lane!
First I'm going to have to educate you! Who the hell are the Koopalings, anyways? Well, if you're a subscriber to everything Nintendo taught us prior to Sigeru Miyamato being an asshat a couple months ago, the Koopalings are Bowser's seven (now eight) children, who he has raised and trained to be the elite commanders and generals of his rather extensive Koopa army.
There's just two small problems with Bowser having children at all: We've never, ever seen a Koopa Queen to be the mother of these underlings, and Bowser's whole motivation for attacking the Mushroom Kingdom over and over is because he's in love with Princess Peach. This isn't even something that's merely hinted at. In Paper Mario you can read Bowser's diary, and he's so heads-over-heels in love with the Director of the Damsel-in-Distress Disassociation that lifts her whole freaking castle right into the sky to be alone with her. The guy has some serious rejection issues.
So, knowing this, how is it possible for Bowser to have children? Well, let's start by looking at Bowser's own childhood, as seen in Yoshi's Island, Yoshi's Island DS, Yoshi Story, and Mario and Luigi: Partners in Time.
Bowser, King of the Koopas, grew up in the lap of luxury in an enormous castle somewhere just beyond the border of Yoshi's Island and the Dark Lands. He was raised by his loyal caretaker, Kamek, leader and probably founder of the Magikoopas. This is important, because we never even get a hint of Bowser having parents. Why could that be?
In these same titles we learn where babies come from in the Mario universe. You see, at the very beginning of Yoshi's Island, a stork is seen carrying a pair of twins to their parents when he is intercepted by Kamek and drops one of the children to the island below. These twins are of course Mario and Luigi. It was Mario who plummets, eventually being found by Yoshi, but Luigi and the stork are kidnapped by Kamek and brought to Koopa Castle. Yoshi and the young Mario journey across Dinosaur Land to rescue Luigi and set things right.
At Koopa Castle we finally get our chance to see the young Baby Bowser, with only Kamek in sight. Now let me stop you right there: what did we just learn about babies in the Mario universe?
Oh, right. They get delivered by birds.
So King Bowser Koopa has no parents. He was delivered into the care of Kamek Koopa by a stork at some time prior to the game's events, which is probably how Kamek even knew about the storks at all. This is why in all of these games we never once see Bowser's parents. Not at all.
So what does this mean for his eight young Koopalings?
Well, as I discussed up-post, Bowser's primary motivation for attacking the Mushroom Kingdom is his love of Princess Peach. In effect, this means his primary motivation is loneliness. Now, there's something else we've learned about the Mario universe throughout the games. Do you know what it is? Well, here's a hint: It's the entire civilization of star people living above the world whose only purpose is to grant wishes to the denizens living below.
This could mean that, answering Bowser's prayers to cure his loneliness, the Star Spirits made for him children. These children, like Bowser himself, were delivered in the bill of a stork and have no biological creators. They were created by the magic of wishes, and delivered by a third-party. They do not have a mother.
This speaks volumes about how reproduction works in the Mario universe for a number of reasons. One of these, is that it gives a somewhat cynical insight into the past of Mario & Luigi's parents. The next is that it also answers the age-old question of who exactly Princess Peach's parents are, considering we've never seen or heard from them before either. You see, it seems evident to me, that while some members of the Mushroom World are clearly capable of reproducing physically, others (like in real life) can't for whatever reason. The Star People exist to satisfy this purpose and create children for parents who will devotedly love them but are incapable of creating their own.
This is even more necessary in a world populated by literally hundreds of intelligent species, not all of which will be capable of procreating together, but all of which have the ability and desire to perform interspecies marriage.
So, there you have it. My thoughts on a lot of Mario things in one shot. Koopalings don't have a mom, Mario & Luigi's parents couldn't reproduce, and the Star People exist to magically manifest children, with the storks delivering the babies from their star nursery to their designated parents.
Oh, here's a little more food for thought:
Bowser and Peach have similar childhoods and lifestyles. They are both royalty with marked differences from their subjects, they both lack parents, they are both shown to have been delivered by storks, and they are both raised by caretakers of their respective kingdoms. This could mean that neither the Koopa Kingdom nor the Mushroom Kingdom existed prior to the events of Yoshi's Island, and that Bowser and Peach were created to bring some kind of order and balance to various parts of the Mushroom World.
This would also go a long way to explaining why Bowser would be so attracted to Peach, and why Peach will actively forgive Bowser and go play tennis with him in her own backyard. There is probably some kind of bond between the two of them that has been around since their very "birth" at the hands of the Star Beings, who designed them both for the exact same purpose, at the exact same time.
Alright, everybody. Have a nice day.
