MK64 rival RNG is done during the character selection screen. The number of frames you spend on that character selection determines your primary and secondary rivals.
This is the rival RNG for some characters in order from selecting them as soon as possible (with 1 controller/d-pad only) and going down 1 frame later at a time.
Mario:
Wario, Luigi
Toad, Bowser
Toad, Wario
DK, Toad
DK, Wario
Bowser, Toad
Luigi, DK
Wario, DK
Bowser, Peach
Yoshi, Peach
DK, Luigi
Toad, Bowser
Yoshi, Bowser
Wario, Bowser
DK, Luigi
Luigi, Bowser
Yoshi, DK
Peach, Wario
DK, Bowser
Wario, Peach
Toad, Yoshi
Luigi, Toad
Yoshi, Peach
DK, Toad
Bowser, Peach
Peach, Toad
Peach, Luigi
Toad, Luigi
Yoshi, Peach
Peach, Bowser
Luigi, Peach
Toad, Peach
Toad, Wario
DK, Bowser
Yoshi
Luigi, Bowser
Wario, Luigi
Toad, DK
Mario, Wario
Toad, DK
DK, Mario
DK, Toad
Mario, Peach
Peach, Toad
DK, Luigi
Toad, Bowser
Bowser, Mario
Bowser, Wario
DK, Luigi
Bowser, Peach
DK, Bowser
Wario, Peach
Bowser, Luigi
Wario, Peach
DK, Luigi
Toad, Wario
Peach, Bowser
DK, Toad
Peach, DK
Toad, DK
Peach, Luigi
Toad, Luigi
Peach, Wario
Bowser, Wario
Mario, Luigi
Peach, Luigi
Wario, Mario
Mario, Bowser
Peach, Toad
Toad:
Wario, Yoshi
DK, Wario
Yoshi, Bowser
Wario, Yoshi
Luigi, Yoshi
Yoshi, Mario
Yoshi, DK
DK, Luigi
Luigi, DK
Bowser, Luigi
Mario, Yoshi
Luigi, Peach
Bowser, DK
Wario, Peach
Yoshi, DK
Luigi, Wario
Yoshi, Peach
DK, Mario
Bowser, Peach
Peach, DK
Mario, Peach
Mario, Luigi
Yoshi, Peach
Peach, Bowser
Wario, Mario
Peach, Luigi
Wario, Mario
Mario, DK
Bowser, Mario
Mario, Luigi
DK, Wario
Luigi, Wario
Yoshi, DK
DK, Yoshi
Luigi, Mario
Yoshi, DK
Mario, Bowser
Wario, Peach
Luigi, DK
Bowser, Luigi
Mario, Bowser
DK, Wario
DK, Wario
Luigi, Yoshi
Wario, Mario
Yoshi, Mario