In Australian English (non-rhotic) the word "air" is pronounced /eː/, in Canadian English (rhotic) it is pronounced /ɛɹ/ and most other dialects pronounce it as somewhere between those two. All the words I know of with that sound have an "r" as part of the spelling of the sound, e.g. hair, care, there, bear, aeroplane. Are there any words which have the same sound where the spelling does not include an "r"?
This is the only word I could think of/find online with the same pronunciation that isn't spelt with an 'r'. There are a lot of different endings with this pronunciation, but this is the only one which ends with "-eah". (There are probably more words with the sound in the middle, but it was harder to search for them.)
Maybe it's not a coincidence that the only word which doesn't have this pronunciation because of a non-rhotic accent is an interjection!
I'm answering under the assumption you're talking about /eə/ as shown here.
I haven't encountered any words without the r spelling pronounced this way in general, but I have in some American accents. I've heard words like ma'am and damn said this way in particular.
I hadn't heard the term before, but Google came up with "æ tensing", and a good bit of information about it.
No such thing as an "American accent" to the poster other than me who had written that.
The reason why is because the United States houses millions of people, most of which are from different backgrounds and cultures too.
Anyways, some words to answer O.P.'s question are "echo," "echolalia," "echondriac," and even "echelons".