Accurate estimation of central tropical Pacific (CTP) climate variability on interannual to centennial time scales is required for robust projections of future global climate trends. Here we outline an approach that blends instrumental and coral proxy observations to yield a continuous, monthly resolved record of climate evolution in the CTP spanning the past 160 years. We concatenate coral oxygen isotope (δ18O) records from multiple living and fossil corals collected from Fanning Island (4°N, 160°W) and Palmyra Island (5°N; 162°W) located in the heart of the El Niño–Southern Oscillation. We use the regularized expectation maximization (RegEM) method to impute missing data across short gaps of 5 to 23 years within and beyond individual coral records. The resulting monthly resolved Fanning/Palmyra Island climate record spans continuously from 1863 to 2016 and provides an example of how extended time series can be built from shorter coral segments. The extended record highlights the strong trend toward warmer and wetter mean conditions in late twentieth century, in agreement with the majority of climate model hindcast simulations. The continuous reconstruction also enables a direct comparison of four exceptionally strong El Niño events (1877–1878, 1940–1941, 1997–1998, and 2015–2016). Three of these very strong El Niño events in the CTP featured a precursor warm event in the prior year and that may have favored the development of a strong El Niño event.