All of the following are correct and would all communicate essentially the same meaning: The boys need to settle it and will not receive assistance in doing so. (Alternatively, the speaker might intend to communicate If it's going to be settled at all, you'll need to do it yourselves.)
The only exception is that among or amongst would generally not be chosen if only two boys are being addressed.
Not all good or educated writers and language experts agree with the commonly-held idea that between cannot properly be used to indicate relationship between(!) more than two people. See below.
Amongst is more frequently used in British English than in American English, in which among is preferred between the two.
You, boys, must settle it between yourselves.
You, boys, must settle it among yourselves.
You, boys, must settle it amongst yourselves.
You, boys, must settle it for yourselves.
You, boys, must settle it by yourselves.
You, boys, must settle it yourselves. (No preposition is needed.)
Regarding between, among, and amongst, see the usage note at between in The American Heritage Dictionary.
Also see https://english.stackexchange.com/questions/37636/between-vs-among. I particularly recommend @tchrist's thorough treatment of this question in his answer there.
The six options were identified by @snailboat in an ELL chatroom. But all elaboration on them is mine. Thanks, snailboat!