Looking on the internet deeply has found these results:

difficulty in is the most popular phrase on the web.

difficulty with 112,300,000 results on the web	difficulty in 143,500,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	He had no difficulty in finding the place. On the contrary, Miss Mackay experienced... the utmost difficulty in persuading me to stay. I myself have some difficulty in understanding the reason for rejecting this report. They have presented the greatest difficulty in 2000 and 2001. The relatively low implementation rate reflects the difficulty in planning payment needs. Government finance statistics of these annual data progressed without difficulty in 2002. Unexpected curfew presents difficulty in reaching it unnoticed. Victims of Chernobyl have faced considerable difficulty in getting recognition.

difficulty with

112,300,000 results on the web

difficulty in

143,500,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

He had no difficulty in finding the place.
On the contrary, Miss Mackay experienced... the utmost difficulty in persuading me to stay.
I myself have some difficulty in understanding the reason for rejecting this report.
They have presented the greatest difficulty in 2000 and 2001.
The relatively low implementation rate reflects the difficulty in planning payment needs.
Government finance statistics of these annual data progressed without difficulty in 2002.
Unexpected curfew presents difficulty in reaching it unnoticed.
Victims of Chernobyl have faced considerable difficulty in getting recognition.