Consider these two lists of words:
- irresistible, convertible
- comparable, breakable, stretchable
Is there any kind of rule that tells you when it is “-ible” and when it is “-able”?
And then there is likeable versus likable, and sizeable versus sizable - apparently the spelling without the E is North American.
But is always manageable, and never, ever managable, wherever in the world you are. I.e. in words ending in an E, you can sometimes drop the E when adding an -able, bit not always.
Once again, are there any rules to get through this mess? I ask because I keep on getting it wrong, and every time I have to use an -ible/-able word, I have to go look it up, and I can never seem to get them committed to memory.
The general rules for how to determine whether –ible or –able should be used is explained here, though of course there are exceptions, as always.
The likeable/likable, manageable/managable, etc. is indeed one of US versus civilised spelling. The US reinvented English spelling for the sake of efficiency—or so it is claimed—and many of the abominations it inflicted as part of that endeavour have managed to permeate the world, chief among them the obsessive use of –z– instead of –s–. (In the process, they somehow managed to make the spelling of whisky more cumbersome.) There’s a saying that the US and the UK are two nations divided by a common language.
Root words ending in a soft and/or sibilant consonant (–c, –g, –s, –z), followed by an –e (e.g., erase, dance), or where the –e modifies the pronunciation of a preceding vowel (e.g., range, prise), typically retain the trailing –e before appending –able, but again there are exceptions.
'Luthon64
A rare case of Google somehow failing: when I searched for a rule, I searched for something very much like the title of that article ("When to use -able and -ible?
"), and Google failed to find anything.
Looks like it will be an ongoing battle anyway. 
Ha, yes, Google’s search terms have some peculiarities of which the user needs to be aware. Prepending a minus sign before a term means, in Googlespeak, “exclude that term from the search results,” ergo the failure. A leading plus sign means “search results must include that term,” and a phrase in inverted commas means “search results must include that term verbatim, i.e. no derivatives/declinations/synonyms.”
'Luthon64
Well, that solves the mystery then. A, erm, solvable mystery.