The correct quantifier to use in this sentence is 'a great deal of'.
Therefore, the correct answer is:
There was a great deal of rain in the days after the earthquake.
Explanation:
* 'Many' is used with countable nouns (e.g., 'many cars'). 'Rain' is an uncountable noun.
* 'A couple of' means 'two', which doesn't fit the context of a large amount of rain.
* 'Several' implies more than two but still a limited number. 'A great deal of' indicates a large quantity of something uncountable, like rain.