I am not very familiar with the Dutch constitution, but, other than exclusion from the line of succession for marrying without the consent of Parliament, I believe the only option for Amalia to renounce her sucession rights would be a bill introduced on behalf of the King under Art. 29, but that would require approval of two-thirds of the votes cast in a joint session of the two houses of Parliament.
Technicalities aside, the relevant point to convey, especially for readers who live in republics, is that it is generally impossible for a person to unilaterally renounce his/her succession rights to a Crown. So being a successor to the throne is something a person is generally stuck with regardless of his/her will.
Again, countries like Spain, Netherlands and the UK require special legislation for excluding successors by renunciation (in Spain and the Netherlands, qualified majorities are required; in the UK, consent from other Commonwealth realms is also needed). In some other monarchies like Sweden or Denmark, renunciation by ordinary legislation may not even be possible and, again, other than exclusion by unapproved marriages or religious tests, it may be the case that only a constitutional amendment procedure could change the line of sucession (not sure about that though).