Make him an offer he can't refuse
The 'offer' being 'do as I say or I'll kill you'.
This is the best-known line from The Godfather book (1969) and film (1972), both written by Mario Puzo. In fact, it is one of the best-known lines in any film and ranks second only to 'Frankly, my dear, I don't give a damn' as the most celebrated quotation from an American film. The 'offer he can't refuse' line is used in all three films of the Godfather trilogy but varies slightly throughout and isn't always easy to hear through all that cotton wool.
The expression 'make an offer he can't refuse' does occur in literature and film prior to 1972, but not with the meaning that it has now taken on because of its use in The Godfather. For example, Jason Robards' character in the 1934 film Burn Em Up Barnes uses "I'll make her an offer she can't refuse". The meaning there is quite different. The character is suggesting making a large and tempting offer of cash - it is meant to be taken as generosity rather than as a threat.
Puzo appears to have been making an reference to an existing phrase so that the Godfather character could ironically pretend that his 'offer' was benevolent.
In the first occurrence in the first Godfather film, it is 'I'll make him an offer he can't refuse'. In one of the film's best-known scenes Don Vito Corleone (Marlon Brando) is visited by his godson, the famous singer Johnny Fontane (Al Martino) - a characterization that is widely believed to be based on Frank Sinatra, although many people associated with Sinatra and the film have denied this. Fontane asks for Vito's help to secure a film role that will boost his fading career. The head of the film studio, has previously refused to give Fontane the part, but Don Corleone tells Johnny:
"I'll make him an offer he can't refuse."
The studio head later wakes to find the severed head of his expensive racehorse in his bed. Unsurprisingly, Fontane is subsequently given the part.