Which is correct? “The students had a difficulty in getting the books” or “The students had difficulty……?

The second sentence is correct; you do not normally say `had a difficulty’. The word `difficulty’ does not take the indefinite article `a’ before it. For example, we say, “The children had difficulty in understanding the accent.” We don’t say, “The children had a difficulty in understanding the accent.” It is possible to drop the word `in’ in the sentence.

Example: It rained heavily last night, and we had difficulty (in) finding a taxi.

Source: ‘Know Your English’ ( The Hindu) -April 23, 2007