Why didn't Sirius want to be the Potters' secret keeper?

Because Sirius knew Voldemort would think it would be him, and therefore target him to get the information. That's why he thought Pettigrew would be a better choice, as he seemed to be such an unlikely candidate.

He berkata that he didn't believe that anyone would guess the Secret Keeper would be Pettigrew. Sirius would just be the obvious assumption. I also got the impression he wasn't sure if he'd be able to resist betraying them under the Cruciatus curse (if betraying the Fidelius Charm can be done under torture)