What can I give my 3 yr old for constipation?

Prune juice. I would try a little prune juice diluted with water. Dilute one half water and one half juice. Then if doing ok it is safe to use daily. You can always keep using less water over a few weeks until better. Make sure lots of safe liquids used a lot but not just before bedtime. Raisins should work and other natural laxative foods as you likely know. Do not use laxative! see md if still an issue!
Benefiber/prune juic. Prune juice is quite safe, but does not taste very good and so tough to get a 3 yr old to take. Benefiber cmes in powder form which can be mixed in water, juice/milk, spinkled on foods..Clear when mixed in water etc...No taste, no odor, thus will likely be more palatable to young children. It is safe and good for the bowel as well. If symptom is severe, get evaluated by doc...Good luck.