There are a number of systems for citing various materials (MLA, APA, etc.). These vary by discipline, country, journal, level of formality, and so on. Obviously one should know which system should be used for citing a particular source.
That said, when is it best to use the phrase "courtesy of…" when citing? If it isn't ever best, when is it acceptable?
If it matters, let's narrow the context to presentations/lectures.
Best Answer
It's best when you've asked the owner of the rights to the material cited (literature, generally) or used (graphics, generally), and that owner has not only given permission but also asked you in return to use that particular phrase to credit the owner.
It's acceptable when you've asked the owner of the rights and the owner has given permission without specifying any particular phrase to use when giving the owner credit.
As requested, this answer omits mention of style guidelines from whatever source (MLA, APA, publishing house, journal, etc.). Where those exist and conflict with the phrasing you've asked about, of course the style guideline would take precedence.