What Carl said about using the slowest speed available. A slower speed on the press will enable the motor to keep going. Unless the belt is what's slipping, then it needs to be adjusted tighter. Look for letter size drills around 11/32 inch. You didn't say if you need smaller or larger drill sizes, but there are some on either side of 11/32.
Here's a chart of the sizes available between 5/16" and 3/8" (you can ignore the metric sizes, as they're probably much harder to find.) The second column is the drill size in inches.
Kevin 1951 Chevy 3100 work truck Follow this saga in Project Journal Photos 1929 Ford pickup restored from the ground up. | 1929 Ford Special Coupe (First car) Busting rust since the mid-60's If you're smart enough to take it apart, you darn well better be smart enough to put it back together.