Is there any correlation between La Niña/El Niño and seismic activity?
There is a case study from Environmental Science entitled El Niño: A Link among Atmospheric, Oceanic, and Crustal Circulation? that discusses  the correlations between seismic activity and El Niño cycles in certain areas of the world, that have been documented:


  A geophysicist, Daniel A. Walker, hypothesizes that a different sequence of events produces an El Niño event. Walker says that the thermal input to the oceans comes from Earth’s interior. This hypothesis is based on an intriguing correlation of seismic activity under the eastern portion of the Pacific Ocean near Easter Island and the onset of El Niño events. This correlation can be used to illustrate possible linkages among the physical systems of planet Earth and the difference between statistical correlation and physical causation.
  
  The East Pacific Rise is located west of Easter Island. Along this rise, tectonic plates move 160–170 mm (6.3–6.7 inches) per year. This rate is one of the most rapid in the world. As a result, seismic activity along the East Pacific Rise has been studied extensively for more than thirty years. During this period scientists have tracked the number of earthquakes and the amount of energy they release.





  Months with the greatest number of earthquakes or months with earthquakes that release the greatest amount of energy precede the onset of El Niño events. This hints at a relationship between seismic activity and El Niño events. A simple statistical analysis suggests that if the seismic events and the El Niño events occurred randomly, the probability of finding a sequence in which periods of heightened seismic activity precede El Niño events would be 1 out of 313. Such long odds imply that the sequence probably is not generated by random chance. Rather, there may be a physical connection between seismic activity and El Niño events.
  
  But statistical correlation should not be confused with physical causation. Correlation indicates that the timing of the two events is similar but does not mean that the two events are connected. 
  
  Scientists have come up with several explanations for how seismic activity may trigger El Niño events. These hypotheses are based on the relationship between air temperature and pressure. In general, warm air has less pressure than cold air, so hypotheses seek to explain how seismic activity along the East Pacific Rise could affect air temperature.


There are several other articles that discuss the relationship between La Niña/El Niño cycles and seismic activity, such as this article published by RSTA entitled Statistical analysis of the El Niño–Southern Oscillation and sea-floor seismicity in the eastern tropical Pacific.

There also appears to be a relationship between El Niño cycles and volcanic activity, as published in Nature.