One way in which it is possible to mine for argumentative topics about John Donne's poetry is to take a look at parts of his life to see how they might have influenced his style or choice of topics. The most obvious argumentative topic when taking this approach would be to discuss the possibility that Donne's Catholic background was the most important element of his metaphysical style and concerns.
Donne was raised Catholic but converted to Anglicanism later in life. No one is exactly certain why this was the case, but many speculate Donne knew his career would never flourish in an openly anti-Catholic England. Some argue there is a sense of guilt that comes from this part of his biography in his poetry. Choosing this as one's topic would involve biographical research and finding similar arguments by other scholars for or against this interpretation. It would also require a careful selection of poems and sermons from Donne which best show this possible conflict.
Another type of argumentative subject could be the question of Donne's influence on later writers. His work was rediscovered by the modernists in the early twentieth century after centuries of neglect. One could argue why this was the case; what about Donne's poems resonated with the modernists' beliefs and formal styles, especially since modernists tended to be skeptical about religion or even the existence of God? This approach would require at least a basic familiarity with modernist poetry such as the work of T. S. Eliot and Ezra Pound.