General Antonyms:
* Carelessly
* Negligently
* Roughly
* Hastily
* Sloppily
* Casually
* Perfunctorily
More Specific Antonyms:
* Superficially (if "meticulously" implies thoroughness)
* Randomly (if "meticulously" implies a specific order or method)
* Imprecisely (if "meticulously" implies accuracy)
* Carelessly (if "meticulously" implies taking care with details)
The best antonym will depend on the specific context in which you're using the word.