Cut a hole in the top of the watermelon, wide and deep enough to insert a funnel. Pour in as much vodka through the funnel as can be absorbed (1/2 to 1 cup). Remove the funnel and replace the watermelon plug. Let sit for 4 hours.
Again, pour in as much vodka as can be absorbed. Repeat the process until all the vodka has been absorbed. (The watermelon flesh gradually will absorb all the vodka.) Refrigerate until well chilled. When ready to make the daiquiris, cut the watermelon in half and scoop out the flesh.