What are operad automorphisms? What is the general concept of an *operad automorphism*$?$ Is there a "standard" definition?
[added after comment] If an operad automorphism is an invertible operad endomorphism, how then is operad endomorphism defined? 
I'm being drawn into these ideas for a section of a paper I'm workign on and most likely this is written-up nicely somewhere,so

references would be most welcome.

 A: I'm not sure what the question you're trying to ask is, but the answer to the question that you have asked is that an operad automorphism is an invertible operad endomorphism.
[EDIT] (just restating Ryan's comment on the original post)
An operad endomorphism is an operad morphism where the source and target operads are the same.  An operad morphism is a collection of maps $\mathcal{O}(n)\rightarrow\mathcal{P}(n)$, one for each arity, such that the obvious squares involving the operad structure maps commute.
[/EDIT]
Perhaps you want to know about operad automorphisms in a homotopy category.  In that case you want to understand what an operad quasi-isomorphism is.  This is an operad morphism which is a quasi-isomorphism on each underlying space of operations.
Would you like to refine the question?
A: Suppose we only care about operads in chain complexes, although i think this can all work more generally. Then an operad is a monoid in the category of symmetric sequences with respect to a particular monoidal product. so a morphism of operads would then be a morphism of monoids. I think this framework might help clarify things. The reference I have in mind, although i am sure there are earlier ones, is Kathryn Hess's lecture notes on the cobar construction. You want to look at the second lecture, page 9 specifically.
This different monoidal product is just what you want it to be in order for a monoid to be an operad! I would explain more, but I can't do any better than Hess: 
http://sma.epfl.ch/~hessbell/Minicourse_Louvain_Notes.pdf
PS: a symmetric sequence is a functor from the groupoid $\Sigma$ (where the objects are sets {1}, {1,2}, ... {1,...,n},... and the morphisms are bijections) to chain complexes.
