I've been actively looking for another job, but I don't want to tell my current boss until I've lined up my next position. The problem is that I've been going out on a lot of interviews, and I'm starting to run out of excuses for missing work. What's the best way to juggle this stuff?
On the plus side, since you are currently employed, you are able to search from a position of strength. You can better afford to wait for the best opportunity for you, and it would be unwise to do anything to disrupt that. You are probably right to be discreet in your job search activities. However, while discretion may be called for, it sounds as though you aren't going far enough.
Trying to conduct a career search during "Extended Lunches" or "Doctors Appointments" is not only unethical with respect to the time your employer may be paying you for in good faith, it can also quickly tip your hand before you are ready. If your supervisor is even marginally aware of your typical patterns of activity, a sudden and significant change will indicate that something is up.
When scheduling interviews, it would be better to see about scheduling something before or after your normal work hours if possible. Often, potential employers can work with you if you explain your situation. Emphasize your strong work ethic and your commitment to delivering a full days work for a full day's pay, and you can even turn this into a selling point that will put you ahead of other candidates being considered.
By being upfront, you may also prevent an embarrassing call to your current employer for purposes of reference checks.