The correct method of alerting a user accessibly should be to conform to the WAI-ARIA (Accessible Rich Internet Application) Specifications. Now the documents are only the technical part of your implementation - as with all Internet technology its implementation among screen readers and other accessibility tools varies widely and is difficult to ascertain without extensive testing, but it is certainly the best we've got to work with as of now.
The specifications calls for this type of messages to be marked with the role='alert'
, and their dialog boxes with the role='alertdialog'
attribute. It states that alerts are
A message with important, and usually
time-sensitive, information.
which would certainly fit the bill. Now I'm not sure about your concern about the screen reader buffer problem, but as far as my reading on this subject goes the screen readers that adopt the WAI-ARIA specifications will need to be constantly scanning the page for new attributes and elements, as tutorials like this show, it is even possible to add the alert
attribute to elements already present on the page, thus I do not believe that your concern should present a problem to modern screen readers.