General opposites:
* Responsible
* Accountable
* Trustworthy
* Dependable
* Reliable
* Conscientious
* Mature
* Disciplined
* Careful
More specific opposites:
* Thoughtful (opposite of impulsive)
* Careful (opposite of reckless)
* Considerate (opposite of inconsiderate)
* Organized (opposite of disorganized)
* Prepared (opposite of unprepared)
The best opposite will depend on the specific situation and the meaning of "irresponsible" in that context.