0-2
Children this age most often cry when in any kind of distress. That's how they let you know, without words, that they are cold, hot, wet, gassy, hungry, etc. In a child who experiences a grief reaction (and yes, in the field we'd call it that....it's traumatic to lose anyone at any age), you'd see crying and general crankiness, but you'd also see a fussiness to get more attention. This could turn into temper tantrums or extreme bouts of crying (lasting anywhere from an hour to three) where they are inconsolable. Small infants and toddlers will also show variance in their eating and sleeping patterns, perhaps being more picky, have trouble latching on, or frequent night wakings. Toward the end of this age range, children will show regression in behaviors and skills they have already learned, like toilet training, walking, and language.
2-4
Preschool-aged children will also show regressive behavior, just like the above age range. They could be completely potty trained, but regress back to using pull-ups when faced with a traumatic grief situation. These children could show anxiety, specifically when having to be separated from a parent or caregiver. They might be clingy, grabbing on to the legs of their safe person, when faced with being separated. Crying is also common. Children this age might be aggressive, when they weren't so much before. This is an adjustment reaction to the trauma, and with appropriate intervention, as we'll discuss next week, should eventually dissipate. This age range obviously has more language skills, and as such will openly talk about death and try to make sense of it.
5-8
School-aged children could develop school phobias, withdrawal from friends, or learning problems they didn't have before. They might also exhibit aggressive behaviors, especially boys, who tend to show an increase in destructive behaviors. Children this age might be more prone to stuffing their emotions so that they appear to be okay to peers. They might be more clingy to caregivers, though. The emotions they do have might be excessive guilt or denial, both of which are common. Children are ego-centric beings, thinking the world revolves around them, so they take undue weight upon their shoulders. It's also at this age that psychological symptoms might manifest more as physical symptoms, such as hurting tummies, headaches, etc.
9-12+
It's very common for emotional reactions to be kept silent at this age. If the youth as an outlet (counselor, church group, sports) they might find their emotional needs met. If they don't, then unresolved grief can lead to "acting out" behavior, such as drugs, criminal activity, and risk-taking (pushing their body to its physical limit). Two common polar opposite reactions I've heard from teens: "I just want to feel something" or "I just want to numb out." For those teens who are more likely to be emotional, there can be overt depression, withdrawal, guilt, anger, and denial. They might lack motivation to do anything, grades could drop at school, or things they once found pleasurable don't appeal to them anymore.
Hopefully this has helped flesh out some common reactions. There are other behaviors that might exist that haven't been explicitly listed, and each child's grief is unique. Environmental factors like previous exposure to trauma, responsiveness of caregivers, and internal resiliency of the child can make reactions more or less intense and/or severe. Be sure to write-in with any specific questions, using Friday's Dear Jeannie column.