Watermelon rind - Cut away most of the hard green exterior and pickle the white part with a standard brine and whatever spices you desire.
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Green beans - Green beans can be blanched in boiling water for two to three minutes and then shocked in an ice bath to preserve their color through the pickling process.
Grapes - Pickled grapes sound strange, but are actually a luxurious addition to a cheese board. The key is adding warm spices to the brine instead of tart ones.
Cherry tomatoes - Pickled cherry tomatoes add so much brightness to salads and even cocktails.
Yellow squash - You don't see pickled squash very often, but it does well with a simple brine and some onion and garlic. Slice them thinly and use them in sandwiches or on burgers.
Asparagus - You can blanch the asparagus in boiling water then shock in an ice bath to preserve the color and crunch. The brining process goes nicely with garlic, turmeric, and black pepper.
Corn - The sweetness of the corn plays well with the vinegar brine, and you can either cut fresh corn from the cob and then cover it in a warm pickle brine, or use baby corn.
Carrots - You can cut them into slices, thin shavings, or sturdy spears, and they taste amazing when pickled with things like coriander, ginger, turmeric, and thyme.
Peaches - Under-ripe peaches, as well as fruit like plums and pears, do really well with a brine that uses apple cider vinegar. Peel and slice the fruit and use both salt and sugar in the brine.
Garlic - Spicy pickled garlic grew very popular on the internet in recent times, and it mixes the pickled garlic with hot sauce (usually Sriracha), chili powder, dried thyme, and honey.