They were sparse. There was no exchange of ambassadors from the founding of the United States until 1870, with only minimal relations during that time. With the loss of the territory of the Papal States in 1870, relations between the papacy and the US were effectively cut off. Technically diplomatic relations were not reinstated until 1984 (Though there were some presidents that named personal envoys to the papacy starting with FDR in 1933). In general there was a large amount of anti-Catholic sentiment in the US in the post-US Civil War era, and the papacy was much more concerned with events closer to home (the "Roman Question," nationalism, communism, etc) than they were a with a nation across an ocean. Interactions were quite rare between the two bodies until the 1930's. A visit by the US Postmaster General opened some doors in 1933 during the pontificate of Pius XI. In 1936 Cardinal Secretary of State Eugenio Pacelli visited the US and was warmly received by FDR, as well as visiting much of the nation in a whirlwind airplane tour. The personal interaction between the sitting US President and the visiting head of foreign policy for the Vatican made later relations possible--particularly when Cardinal Eugenio Pacelli was elected Pope Pius XII in 1939. That took place in March, and many place the beginning of WWII in September with the invasion of Poland by Germany. In those few months very little happened, and FDR's personal envoy to the papacy (Myron Taylor) wasn't named until December of 1939. And with that, we've hit the time limit of pre-WWII.

I hope that answers your question. Followup questions from OP and others are always encouraged. I must warn that I am more familiar with the 20th century papacy. You can find much of the correspondence between FDR and Pius XII in a number of places, but that falls outside the timeline defined by OP.