The second.

Most people associated with horticulture that are familiar with the plant in question would pronounce it as cotoney-aster. But you have to remember that plant names are frequently an amalgamation of several languages. 'Botanical Latin' is mainly a written language and a particular name can in fact sometimes be a combination of Latin, Greek, English or French etc etc. Convention will often have a name said in a certain way but that doesn't necessarily mean there is a correct way. There is also a certain amount of 'snobbery in certain areas of the 'horticultural world'. Botanical names can be a little irksome especially to those starting out in the plant world but they are a 'necessary pain in the backside' as common names can cause such confusion (for example bluebells in Scotland are a different plant to bluebells in England). Once you become familiar with botanical names they can tell you a great deal about a plant from the species, variety or cultivar name applied to it. I'd say enjoy your plants but don't get too bogged down with the 'correct pronunciation or the nomenclature' unless it is your profession.
Cheers Jan

The great thing about garden web is that no one can hear how you pronounce a botanical name anyway :-) So many of the botanical names we pearn first from books, which don't give us much of an idea about the pronunciation. When you do hear the word spoken, you may not even recognise it because of the difference in the way it is said, compared to the way you perceived it. There is even considerable difference in pronunciation between 'English' speaking countries. Clematis is a prime example. The accent may go on the first or second syllable, depending where you are from.
Yes there is a lot of snobbery, but it isn't really justified. We all have to learn!

I tend to agree with Jan. Pronounce it with what you are comfortable with.