There’s not typically any enforced delay between the posting of a single tweet to the next on a user account. All user accounts have daily posting limits that are broken down into roaming periods throughout the day, but an account has to be tweeting at a pretty good clip to cross over those.
In what way is the posting not being allowed? Is there a specific error message you’re getting from the API disallowing it? Is the tweet text significantly different than the last few posts? Twitter detects for duplicate tweets from a small handful of the user’s recent tweets.