Eye-ree-nee sounds cutesy to me. I’ve heard it pronounced ear-reh-nay before, but I think I prefer just plain [name]Irene[/name].
“Eye-ree-knee” just makes me think of irony. Plus it would never be pronounced correctly if you went that way, I’ve only ever heard it said as “Eye-reen”.
I accidentally voted yay but I meant to vote nay. I pronounce it EYE-reen. I’ve never heard it the other way.
I’ve never seen [name]Irene[/name] pronounced any way other than “eye-REEN.” Any other pronunciation is counterintuitive, and I think a child with a different pronunciation would be in for a lifetime of correcting people. If “eye-[name]REE[/name]-nee” is the pronunciation you’re after, I’d go with a more phonetic spelling, i.e. Irenie.
oliviasarah, you are totally right! I meant to place the emphasis on eye-[name]REE[/name]-nee, rather than EYE-ree-nee, but my hormonal, tired brain got the best of me. 
I’m going to edit the OP to reflect this and try to edit the poll.
Thanks for your input, everyone! Keep the opinions coming! 
Oops, sorry for misinformation earlier, I appreciate those who actually know for correcting what I said, thank you!
Never heard of [name]Irene[/name] being pronounced eye-ree-nee… I think it sounds best as eye-reen & I voted yay based on that pronunciation.
Yea I pondered the “Its used in [name]Britain[/name]” too - I can see two Brits have already answered, one from Liverpool and one from Yorkshire - I live in the other end of [name]Britain[/name] from them and have never heard EYE-ree-knee either.
I know a girl name “eye-[name]REE[/name]-nee” Ireni.
I think it’s a quirky sort of name, rather feminine- I like it.
[name]Irene[/name] is eye-reen to me.
I absolutely adore eye-ree-nee! I think it’s beautiful. I voted yay, although I think she’ll get eye-reen most of the time. Unfortunate, really, because the former is so much prettier imo.
Reading other posts, I’m also from England {central, an hour or two slightly north west of London}. I’ve heard both pronunciations: I always here eye-reen on elderly women, but eye-ree-nee on young girls.
That’s strange you say that, because as a [name]Brit[/name] I’ve never heard the three syllable pronunciation of the name, only EYE-reen or eye-REEN (I’ve heard it emphasised on both syllables, but never with an extra one.)
I know an [name]Irene[/name] nn [name]Renee[/name] (ree-nee) though, so if you want the eye-ree-nee prn maybe just go with ree-nee for [name]Renee[/name] instead. You’re more likely to get people to say ree-nee rather than ren-ay than you would trying to get eye-ree-nee rather than eye-reen.
I’m with [name]Blade[/name] on this one. French pronunciation is the loveliest. 
I pronounce it the [name]German[/name] way: e-reh-neh. It’s very soft and gorgeous.
I prefer of the two you presented:
eye-reen.
I’ve only heard it pronounced eye-rene (my preferred pronunciation) and ee-re-ne (Spanish pronunciation).
Eye-ree-knee doesn’t sound that pleasant to me, probably because of the repeating “ee” sound.
I don’t like it. [name]Irina[/name] with the nickname [name]Irini[/name] wouldn’t be bad though.