"Reasonable diligence" means putting in a sensible and careful effort to complete a task or achieve a goal. It involves doing what is reasonably expected of you, while being thorough and persistent in your actions. Full definition
The evidence could have been obtained with reasonable diligence for use at the trial. (newlawjournal.co.uk)
There is also a defence to the charge that you did not know or could not ascertain with reasonable diligence who was driving at the time of the offence. (tvedwards.com)
Are there any provisions for copying if, following reasonable diligence, the copyright owner can't be found? (law.stackexchange.com)