Countries worldwide are facing challenges with increasing the COVID-19 vaccination rates for children. This study examined associations between perceived knowledge, coping appraisal, threat appraisal, adaptive response, maladaptive response, and intention, and possible variance across parents (mother or father) and COVID-19-like symptoms experiences regarding parental intentions to vaccinate their children. A total of 836 Iranian parents with children between the ages of 6 and 12 y completed measures assessing perceived knowledge, coping appraisals, threat appraisals, intentions, adaptive responses, and maladaptive responses. Multigroup structural equation modeling revealed that perceived knowledge was positively associated with both coping and threat appraisals, coping appraisals positively associated with adaptive responses, maladaptive responses, and intentions to vaccinate, threat appraisals positively associated with adaptive and maladaptive responses, and adaptive responses positively associated with intentions to vaccinate. The invariance evaluation revealed no differences across parents or COVID-19-like symptoms experiences in parental intentions to get their children vaccinated. The findings suggest that cogent information regarding childhood COVID-19 vaccination may boost parents’ knowledge influencing their appraisals, adaptive responses and intentions to vaccinate their children. Specifically, coping appraisals and adaptive responses appeared to be important mediators between knowledge and intentions to vaccinate. Furthermore, intentions to vaccinate children may not be strongly influenced by parental roles or COVID-19-like symptoms experiences. These findings may help multiple stakeholders promote COVID-19 vaccination rates among children, and countries should further examine ways of increasing rates based on their specific needs.