Wash the outside of the watermelon well with soap and water. Cut open and remove the flesh (and seeds, if there are any); enjoy the fruit now or refrigerate for later. Cut the rind into manageable chunks and carefully remove the dark skin, leaving behind the white part and maybe a little bit of the remaining fruit. Cut the rinds into slices or chunks about 1 inch thick—you should have about 6 cups. Put the rind in a colander and sprinkle them with 2 tablespoons of the salt; toss well.
Let the colander sit in the sink or in a bowl until they “sweat,” about 2 hours. Rinse the watermelon rind, then pat dry with towels. Put in a nonmetal bowl.
Put the remaining 1/4 cup salt, the vinegar, sugar, and pickling spice, along with 2 cups water, in a pot over high heat. Bring to a boil, then remove from the heat and let cool for about 5 minutes. Pour the brine over the watermelon rind and let cool to room temperature. (Add more vinegar or water in equal parts if rind is not covered.)
Transfer the watermelon rind, brine, and spices to jars or containers; cover with airtight lids. Store in the refrigerator for at least 3 days, longer for stronger pickles. They will keep in their brine for up to 3 weeks. (Unlikely, but if at any point they start to smell funky or get foamy, discard them.)