As a kid, I was a firm believer that the Koopalings were Bowser's adopted kids. I always thought it would be really nice of Bowser to soften up and take in a bunch of orphans and raise them as his own. I still think it would've been a good storyline, but I really don't think that they are his kids in any fashion anymore. They're minions and minions only (although they are among the highest-ranking). Dialogue from recent games, particularly the latest Mario and Luigi games, suggests that there is no parent-child relationship between Bowser and the Koopalings whatsoever. They refer to him as "Lord Bowser" or "Boss" formally, or simply "Bowser" if they're talking casually amongst themselves. This line really sells it:
Bowser is just their boss, and there is no sibling relationship between them and Bowser Jr!
Even when Bowser addresses them in recent games, he always addresses them as a group, as if they were just a squad of minions. Additionally, he always has the same commanding tone he uses when speaking to all his other minions. He completely lacks any of the softness he has when talking to Jr
(unless, of course, he's talking to them about Jr).
Technically speaking, we've never seen any written Koopaling dialogue in the main series since before Sunshine. If ever. So there is a little bit of wiggle room if you want to argue against the canonicity of the M&L series. However, given all the other juicy lore that can be found in that series, it would be a detriment to the Marioverse to consider it non-canon.
As much as I'd like to believe it, I just can't anymore. The facts don't lie.