I find it easy to say, but I sound my r. It might be more difficult in another accent ?
I am non-rhotic. Draw and drawer sound the same.
"There're" just sounds like "there".
In my accent, "there" would sound like the word "air" without the "r" sound, with "th" at the front.
It sound like I am saying "There shoes in the wardrobe" when I try to say "There're shoes in the wardrobe".
Even "They're in the wardrobe" sound like "There, in the wardrobe".
There/Their, They're, There're, all are the same to me.
I probably wouldn't contract it as "There're". I would just say "there are" or, yes, "there's", or even just say "they are in the wardrobe" if the item has already been named.
I know it's incorrect to use "there's" but it just comes out.
It will of course, grate on people.
Similarly, my V's sometimes sound more on the "F" side.
"Do you haf it?"
Another reason why me saying "You could've done it yesterday" sound like I am saying "could of". I am not, I am using the contraction but my Vs can be very soft and F like. 
I know that probably irritates people, too.