This is probably pretty hard to do.
Fundamentally you want to use some parser to predict "what comes next" to display as auto-completion. This has to at least predict what the FIRST token is at the point where the user's input stops.
For ANTLR, I think this will be very difficult. The reason is that ANTLR generates essentially procedural, recursive descent parsers. So at runtime, when you need to figure out what FIRST tokens are, you have to inspect the procedural source code of the generated parser. That way lies madness.
This blog entry claims to achieve autocompletion by collecting error reports rather than inspecting the parser code. Its sort of an interesting idea, but I do not understand how his method really works, and I cannot see how it would offer all possible FIRST tokens; it might acquire some of them. This SO answer confirms my intuition.
Sam Harwell discusses how he has tackled this; he is one of the ANTLR4 implementers and if anybody can make this work, he can. It wouldn't surprise me if he reached inside ANTLR to extract the information he needs; as an ANTLR implementer he would certainly know where to tap in. You are not likely to be so well positioned. Even so, he doesn't really describe what he did in detail. Good luck replicating. You might ask him what he really did.
What you want is a parsing engine for which that FIRST token information is either directly available (the parser generator could produce it) or computable based on the parser state. This is actually possible to do with bottom up parsers such as LALR(k); you can build an algorithm that walks the state tables and computes this information. (We do this with our DMS Software Reengineering Toolkit for its GLR parser precisely to produce syntax error reports that say "missing token, could be any of these [set]")