Since you feel that “appointment” doesn’t fit the “deadline” idea, you'll perhaps have the same issue with “engagement” (not to mention that it, like “date,” also has a ‘romantic’ sense!).
Although it doesn’t necessarily expand the meaning of “engagement” to include any more of the “deadline” idea that it might have already, it is interesting to note, however, that Collins’ “Reverso” site translates:
“engagement diary” as “Terminkalender”.
Personally, I think that “engagement” alone does include enough of the notion of “deadline” to use as a single word to express what you’re after, but perhaps by adding “binding” to it (to get “binding engagement”) you could capture better the notion of “deadline.”
Finally, for a single word that would not require the addition of "binding" to capture the “deadline” idea, you could consider “obligation.”
Although certainly not specific to discussions of times and dates, it can be used in that context (e.g., “Sorry, I can’t come because of a prior obligation”)
1. the act of engaging or the state of being engaged.
2. an appointment or arrangement, esp. to be somewhere or do something at a particular time.
3. an agreement to marry; betrothal.
4. a pledge; an obligation or agreement.
5. employment, or a period or post of employment.
6. an encounter, conflict, or battle.
7. the act or state of interlocking.
1. something by which a person is bound to do certain things, and which arises out of a sense of duty or results from custom, law,
2. something done or to be done for such reasons: to fulfill one's obligations.
3. a binding promise, contract, sense of duty, etc.
4. the act of obligating oneself, as by a promise or contract.
5. a. an agreement enforceable by law. b. a document setting forth such an agreement.
6. any bond, certificate, or the like, as of a government or a corporation, serving as evidence of indebtedness.
7. an indebtedness or amount of indebtedness.
8. a debt of gratitude.
9. the state of being under a debt.
(both from ‘RANDOM HOUSE KERNERMAN WEBSTER’S COLLEGE DICTIONARY,’ with emphasis added to the meanings most relevant to the question/answer)