Answer: Both cucumber and melon vines grow best in a rich soil well amended with ample organic matter. Since the cucumbers and melons consist primarily of water, they also need a consistently moist (but not soggy) soil. A mulch will help with this, as will the old rule of about an inch of water a week from either the gardener or the sky. If in doubt, stick your finger into the soil and see if it is dry or not.
As far as the yellowing, both of these vines are subject to a number of foliar problems including those caused by insects and disease. I can't tell which one it is based on your description, but you may be able to tell what is causing the problem by comparing your plants with the the descriptions and photos in these two websites.
Another option would be to take a sample to your County Extension agent for a positive identification and suggested controls, if any. Their phone number in Suffolk County is 727-7850.
Good luck with your plants!
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