I always go back to the scene with the undertaker, Amerigo Bonasera, at the wedding. The line "Someday, and that day may never come, I will call upon you to do a service for me." That's the whole deal, right there. It's not a threat, not really. It's a promise of a future obligation, but framed as a favor he's doing for you by letting you pay him back later. He establishes a debt on his own terms, making loyalty feel like a mutual exchange instead of extortion. He grants the request first, with this almost solemn gravity, and the loyalty comes from that initial act of perceived generosity. It makes the follower feel chosen, indebted, and strangely honored all at once.
Later, with Johnny Fontane, it's the whole "I'll make him an offer he can't refuse" mentality, but applied to loyalty. He fixes Johnny's problem, but the way he lectures him—'You can act like a man!'—it's paternal. Harsh, but from a place of disappointment, like a father scolding a son who's wasted his talent. That kind of criticism, when it comes from a place of perceived care and investment in your betterment, fosters a different, deeper loyalty than fear. It's the loyalty of a disappointed child wanting to make their parent proud. The quotes themselves are often about family, respect, and business, but the loyalty stems from the performance of those values. He doesn't just say 'be loyal'; he acts in a way that makes loyalty feel like the only logical, honorable response.