If you wish, you may say mourner's kaddish for family members other than parents, especially during shloshim (the first 30 days after burial), since the first 30 days after death are the most difficult for the dead person's soul. 
However, you may say kaddish for anyone even after shloshim ends, if you wish, until the end of 11 months (for a shomer-mitzvot person) or 12 months (for a non-shomer mitzvot person. But in a place where only one person says kaddish, you may not supplant another person who is halachically required to say kaddish.