If this is the set of items that form a "state" of the parser, then you haven't written it down right:
fn_call -> ID . L_PAREN fn_args R_PAREN
assignment -> ID . ASSIGN value
assignment -> ID . ASSIGN container
value -> ID . *missing lookahead set*
You don't exhibit the rest of your language, so we cannot know what the lookahead set is for the rule
value -> ID
Under the assumption that you indeed have a shift-reduce conflict in this state, then the lookahead set must contain "ASSIGN" or "L_PAREN". I can't tell you how to fix your problem without knowing more.
Given that your present grammar has these issues, you cannot fix this simply "adding rules" of any kind, whether they involve line delimiters or not, because adding rules will not change what is already in lookahead sets (it may add more tokens to existing sets).
EDIT: One way out of your problem may be to switch parsing technologies. Your problem is the LALR parsers cannot handle the local ambiguity that you seem to have. However, your overall grammar may not have an actual ambiguity if you look further ahead. That depends on your language syntax but you are rolling you own so you can do as you please. I suggest looking into GLR parsing technology, which can handle arbitrary lookahead; check out recent versions of Bison.