The 'Konjaku Monogatarishu' is a fascinating collection of tales that captures the essence of medieval Japan. While finding a complete English translation can be tricky, there are some excellent partial versions available. Helen Craig McCullough's 'Tales of Ise' provides a taste of classical Japanese literature, though not exclusively from Konjaku.
For a more direct approach, 'Japanese Tales' edited by Royall Tyler includes several stories from the collection, beautifully rendered in English. The Penguin Classics edition is particularly accessible, with annotations that help Western readers grasp cultural nuances. Online, the Japanese Text Initiative at the University of Virginia has digitized some translations, perfect for those who prefer screen reading.