General opposites:
* Careful
* Attentive
* Diligent
* Conscientious
* Responsible
* Thorough
* Meticulous
Opposites in specific contexts:
* Careful (opposite of negligent in driving)
* Attentive (opposite of negligent in parenting)
* Diligent (opposite of negligent in work)
* Conscientious (opposite of negligent in following rules)
* Responsible (opposite of negligent in handling finances)
The best opposite for "negligent" will depend on the specific situation and what you want to emphasize.