William L. Rowe in his paper, "The Cosmological Argument," makes the point that the proponent of the cosmological argument (CA) does not commit the fallacy of composition as is often assumed. The CA Rowe is concerned with is the argument from dependency or contingency of being to a necessary being. Rowe is not defending the CA but rather he is clarifying what the argument is. (To be sure, Rowe is not a theist; I think he considers himself an agnostic).
Often the criticism is that this CA makes an invalid inference. Going from 'all dependent beings of a collection have an explanation for their existence' to 'the collection of dependent beings has an explanation for its existence'. Thus committing a fallacy. This inference, Rowe argues, is not made by proponents of the CA. Instead the argument relies on the Principle of Sufficient Reason (PSR), which is that every existing being has a reason for its existence either within itself or in another. Given the PSR then, a collection of dependent beings must have an explanation for its existence. Now, this is very different from committing a fallacy of composition.
Rowe goes on to challenge the PSR and thinks that it doesn't work, even if it is modified (which he does, thrice), implying that since PSR fails so too does the CA. I'm not convinced that PSR doesn't work, but it is worth the read.