The general consensus of economic historians is not much, if any.

The causes of the Great Depression are argued about a lot, but the consensus is more towards the monetary side: the US Federal Reserve's actions or lack thereof, and the operation of the inter-war Gold Standard.

There was a lively theory of economic criticism in the 1930s and for a few years afterwards known as "liquidationism" that the Great Depression was an overhang from the 'excesses' of the 1920s. But this is no longer held, for a variety of reasons. Some main ones are evidence that the increased prosperity of the 1920s was based on real improvements in productivity, not just debt-financed spending (as was often thought at the time - this was before modern GDP statistics were available) and evidence that the money supply was important. On the money supply issue, Milton Friedman and Anna Schwartz in their 1963 book "A Monetary History of the United States" documented changes in money supply in the USA and linked it to recessions, they documented a sharp drop in the US's money supply in 1929. Work by various other researchers has documented on an international level strong linkages between the timing of a country's recovery from the Great Depression and when it left the Gold Standard (or was never on it), strengthening the monetary causes hypothesis. I expect the unprecedented economic boom years of the 1950s and 1960s post WWII also played a part in disfavouring the liquidationist hypothesis as those boom times didn't end in a Great Depression.

Coolidge has been criticised for not acting more to curb stock market speculation, but a recent paper (Tacoma, 2019) presents evidence that he did seek to talk it down, and lacked powers under the US Supreme Court at the time to regulate directly (Tacoma, pages 368-370). Plus stock market crashes have happened before and since, under a variety of different political systems and political leaders, without being followed by a Great Depression.

Arguably Coolidge could have done things like appointed better people to the Federal Reserve, or been more forceful about the operation of the Gold Standard internationally, but these are arguments in hindsight. Generally people in the 1920s lacked the economic statistics and the economic theories that we have today, much of what we know has been learnt from painful experience.

Sources

Parker, Randall. “An Overview of the Great Depression”. EH.Net Encyclopedia, edited by Robert Whaples. March 16, 2008. URL http://eh.net/encyclopedia/an-overview-of-the-great-depression/

Tacoma, Thomas. 2019. “Calvin Coolidge and the Great Depression: A New Assessment.” Independent Review 24 (3).