I have made pickles from a recipe I had long, long ago. They were dill pickles with mustard seed, garlic, onion, salt, and vinegar. They do involve canning, but they were a big hit. I gave away many jars of them as gifts.
My grandfather made what he called "Open Jar Dill Pickles". No canning involved, but you will need a large crock pot (3 gallon, I think.)
There is also the "Refrigerator Method" that might be what you want.
Try searching for "Open Jar Dill Pickles Recipe" or "Refrigerator Pickle Recipe," then see which ones sound interesting to you.
Good luck. Let us know what you found and how they turned out.