I went through this last year while job hunting. I was also uncomfortable doing it in the parking lot, because we get a lot of foot traffic from other employees, and its not unlikely someone would come up to the car to say Hi.
I chose to drive off the property and go to a nearby park/strip mall and find a quiet place to do the interviews when they were during my workday. I kept any relevant information I needed in the car (notebook, resume, laptop, etc.) while at work so it was super easy to run out and back.
If your current employer is cool with occasionally working from home, that may be an option on the days you have phone interviews. I would intentionally schedule 3-4 phone screens in a single day, then just work from home that day. Edit: As @anotherdave pointed out, this depends a lot on the type of work you do, and you should still absolutely put in a full workday for you current job, presumably by working a bit earlier or later than usual to compensate for the hours you spent doing interviews. It also may be tricky if you need to be able to respond to work requests quickly, so use your better judgement to decide if this is an option for you.
If leaving the office during the day, or working from home is not generally an option, you may need to work with the recruiter to fit your schedule. Generally recruiters understand that the best potential employees tend to already be employed, so they are willing to work with you to set times that work for you. I have done phone screens at both 7:30am and 8pm (my normal office hours were 9-6).