I've had the same problem finding low-dose melatonin in brick-and-mortar stores, but Natrol sells a 1mg dissolving tablet on Amazon. If I need a sleep aid, I break it in half for a ~0.5mg dose, chew it with my front teeth, then hold it under my tongue for a bit before swallowing what's left.
It usually takes 15-30 minutes before I get noticeably drowsy, but I feel no more groggy the next day than if I slept sober.