Hi, I was wondering, when putting your specialization certificate on LinkedIn, under Organization which do you think will most likely lead to a job: Coursera, DeepLearning.AI, or Stanford University? I would think it would be between the last two, as just putting Coursera there doesn’t really stand out. Thanks!
If you have experience in doing the above please comment below 
DeepLearning.AI seems more useful, since putting “Stanford University” in your profile implies that you are enrolled there as a student.
In general that’s not what Coursera provides.
If not explicitly written down, I would consider first the organization represented by the person who signed the certificate, which is normally shown in the title under the signature.
To many courses, Cousera is just a platform, so I would wonder whether Cousera can be considered as the organization at all.
I just write Deeplearning.ai.
If you look all the specializations on the deeplearning.ai courses page, all of them appear with DeepLearning.ai logo except for the Machine Learning Specialization that appears with the Standford Online logo. I’ve only finished the first course, but if you look at the certificate it is awarded by both Standford Online and DeepLearning.AI. If you can, put both, if not, choose whatever you want. Just don’t put the Standford part without mentioning the Online one 
It depends on the given certificate - since its a specialisation awarded by the original organisation, then give it due credit & see Coursera as an intermediary.
Whereas if there is 2 organisations collaborating like Stanford & DeepLearning.Ai then look carefully at the awarded institution as to WHO signed it, was it Stanford or DeepLearning but if its both then you choose.
My opinion: It might be redundant to put both organisaitons unless you want to get recognition from both for your job application or something.
And yes, put Stanford online (if it has that option so as to not be misleading).
Coursera has been coming out with their project courses so in a way, crediting Coursera would not be accurate.
Hope that clarifies! All the best for your endeavours!