Migraines start with the constriction of blood vessels in the brain, followed by expansion (causes the pain). Beforehand symptoms that blood vessels are constricting are vision and mood changes. Some triggers are strong emotions, hormonal changes, allergies, medications.
Like all food suggestions, knowing what the cause (emotional, chemical allergy, etc) helps aid in knowing what to juice.
I have seen a lot of people who have common allergies to gluten, dairy and the like eliminate these from their diet and have success in getting rid of their bad headaches completely. It might be worth it to visit your doctor to get food allergy tests, or better yet, conduct your own by process of elimination. Most of us that have alleriges usually have a sneaking suspicion of what it might be.
Apples, Beets, Blackberries, Broccoli, Cantaloupe, Carrots, Celery, Leafy Greens, Onions
Cayenne, Cinnamon, Dandelion, Feverfew, Garlic, *German Chamomile, Ginger, Lemon Balm, Parsley, Rosemary, *Vervain
*If emotion related (to calm nerves)
I have seen great success with juicing a sprig of rosemary in with a juice drink.
If the cause is dehydration from heat or from excessive alcohol consumption, juicing coconut or drinking coconut water can help restore missing nutrients to ease or banish the pain.