What is a good way to request a manager to let me sleep somewhere for about 30 minutes when I am sleepy, without appearing lazy?
If you are in the US, it's likely that "asking to nap" will call unwanted attention to yourself. While your manager may not conclude that you are "lazy", she/he may still view that request negatively (such as "this person can't deal with his personal life effectively" or "this person is trying to make his personal problems my problem").
Instead, find a place where you can nap during your lunch time, so that others don't need to know. Perhaps an office with a door you can close, or even better, your car. If you choose this route, make sure you have an alarm to wake you up so you don't oversleep.
Work on making sure you get enough sleep at night. Go to bed earlier, party less, watch what you eat, avoid using too much caffeine, especially close to sleeping time, change your lunch contents (perhaps light food will make you less sleepy), visit the doctor and make sure you don't have a physical issue (like sleep apnea). Being unable to stay awake during work hours isn't normal.Being unable to stay awake during work hours isn't normal.
If there is a medical problem here, or if you have temporary issues (such as a newborn at home) - then talk with your manager, and see if you can reach an accommodation. But based on what you have written so far, that isn't the case - it's just a personal nap preference issue, and thus is a home problem, not a work problem.
In my experience, managers don't want you to bring your home problems into the workplace. When you are in work, I'd expect you to be working, except during your breaks. If you are excessively tired and need to nap, you want to find a way to do that on your own time, and try not to impede on your work.
Unless all else fails, don't bring this to your manager's attention.