In a jar with a tight fitting lid, combine coffee grounds and 2 ¼ cups cold water. Stir to combine. Cover and set aside at room temperature for at least 12 hours.
Meanwhile, make coconut ice cubes. Preheat oven to 350 and spread coconut onto a rimmed baking sheet. Transfer to oven and toast until golden, stirring occasionally, about 20-25 minutes. Let cool completely.
In a measuring cup, combine sweetened condensed milk, 2 ½ cups warm water, and a pinch of salt. Stir to combine.
Divide among two 15-cube, 15-ounce capacity silicone ice cube tray. Divide coconut among cubes.
Transfer to freezer and freeze until firm, at least 2 hours.
Strain the coffee twice through a sieve lined with a coffee filter or cheesecloth.
Pour the strained coffee into a large pitcher. Add remaining 2 ¼ cups cold water.