Even if you enjoy your job, having to work a schedule with awkward hours can make life difficult if they conflict with your family or personal obligations. Although you shouldn't expect to be able to change your work schedule just because you're not a morning person, sharing a valid reason with your boss might lead to a better schedule for you.
State Your Case
Request a short meeting with your direct manager and clearly explain why your current work schedule is problematic. Provide specific reasons, rather than just complaining about your hours. Suggest a work schedule that suits you needs but would still allow you to meet your job requirements. Hand your boss your thoughts in a written document so she has a formal account of your request, and follow up in a month if you haven't received a decision.
Reasons and Incentives
Part of appealing to your boss to have your schedule changed is to share precisely your reason for the request, such as having to drop your children off with a babysitter before work, or the need to visit a loved one in the hospital in the evening. Keep in mind that many employees might face similar scheduling issues, so your reason might not be unique enough to warrant a change. To increase the appeal of the change from management's perspective, provide an incentive to your boss when making your request. For example, offer to expand your responsibilities. Additionally, stress how the change will benefit the company. If you want to begin your day earlier, for example, you might be able to get a head start on important daily tasks to ensure they are finished ahead of time, freeing you up for other duties as the day goes on.