Adab! This is interesting; just noticed this thread.
I was mainly joking when I said to spell the two words differently. True, it would help to distinguish them, but then again, as long as you guys know what you're talking about (which you do), there is no special need.
But anyway, the issue (somewhat pedantic, but for interest's sake) would be that the word for "couplet" has the Arabic letter " 'ain " in it. While this letter has a very distinct sound in Arabic, in Punjabi/Hindi, when saying words that derive from Arabic, it is not pronounced per se. Nonetheless, it is retained in the spelling (in Persian-script and sort-of in Gurmukhi-script Punjabi). AND it has some influence on the pronunciation of the word overall. Finally, people that are trained at poetry often try to pronounce Arabic sounds in their Punjabi/Urdu, so it can vary slightly between poetic pronunciation and "regular" speech.
The "r" is the same in both words. (It is not what I would call a "hard R"; that usually refers to a "retroflex R" as in "bhangRa". I'm not sure what faizan meant by "hard R"/"Rra".) faizan has a point when he comments about the "r" in the English words that BRRUAH! compared. However, I think BRRUAH! was emphasizing the difference in vowels between "hair" and "shape", rather than saying that the Punjabi words were EXACT equivalents. English examples, as faizan is noting, do complicate things because the vowels in those words come under the influence of r. Different English speakers will pronounce those vowels differently. The classic distinction is between "merry," "marry," and "Mary." Probably most English speakers in North America have "lost" the distinction between those words in their pronunciation. In New York City and greater Boston, however, people clearly distinguish between the vowel in "merry" and "marry." For others, the "a" in "marry" has come under the influence of "r" in such a way that it sounds like the "e" in "merry". But this is a side issue, not related to Punjabi.
Still, it can be a useful comparison in thinking about how the letter 'ain influence vowels' pronunciation in the North Indian languages.
The words for "tiger" and "couplet" are spelled differently (in Arabic/Persian-script and Gurmukhi), but they are pronounced the same or nearly the same in Punjabi speech. Whereas most Punjabi words are "spelled as they sound", if you feel like spelling "couplet" exactly (for whatever reason - it's up to you), then it is going to "look" different than it sounds.
The spelling of "tiger" in Persian script is, like faizan said, "sheen, ya, ra".
Spelling in Gurmukhi is ਸ਼ੇਰ. Transliteration of both is SHER, where the E approximates the "a" in "plate" (it is not exact, but this is enough reference to know what sound we are talking about!)
Spelling in Hindi/Devanagri is शेर. Corresponds to Gurmukhi.
The spelling of "couplet" in Persian script is "sheen, 'ain, ra". The vowel understood to be between sheen and 'ain is "zer", and between "'ain" and "ra" there is "nothing" or (as I understand) just the default zabar/a sound.
Transliteration of Persian would be SHI'AR (or SHI'R). The transliteration represents the spelling with short vowel I (as in "spit") and A (as u in ~ "cut"). HOWEVER, the vowels come under the influence of the letter 'ain ('), and the I becomes pronounced more like E.
Which E? For some it sounds exactly the same as the E in SHER (tiger). (In fact, in Hindi, both words have become spelled exactly the same, as if to reflect this. Hindi spelling is poor at representing Arabic letters.) For others (to my ear, but I am willing to be wrong!) it is closer to the E in "bet", which corresponds to Punjabi ਐ (zabar-ya in Persian script) which......and here is where big confusion could happen... is formally transliterated at AI. Yes, you are seeing two letters there, but AI stands for just one vowel sound. In Gurmukhi, E versus AI is ਏ versus ਐ.
In Gurmukhi, "couplet" is written as ਸ਼ਿਅਰ and this would be transliterated as SHIAR. Compare this to the Persian SHI'AR above. Gurmukhi has no way to represent 'ain ('), but the 'ain from historically Arabic words is often evidenced in spelling by a ਅ that doesn't seem to belong there!
Pronunciation of this Gurmukhi spelling is again slightly different than it looks. Think of the word ਮੁੰਡਿਆ which is transliterated MUNDIA but which many would write MUNDEA. An "I" is in the spelling, yet people think it sounds like "E"...albeit not quite the E of ਏ, that is, not quite the E of SHER/ ਸ਼ੇਰ.
So, the "I" in the precisely transliterated SPELLING of "couplet", SHI'AR (Persian style)/SHIAR (Gurmukhi style) is pronounced differently in this context (in the context of the surrounding sounds). This I is pronounced either just like E in SHER (as the Hindi-wallahs) or like AI, which is like a slightly "shorter" form of E that is reflected IMO by Gurmukhi's spelling SH-I-A-R rather than SH-E-R. I think both pronunciations are extant and acceptable. Because I hear AI sound, and because "shiar" looks pretty nutty!, I wrote it informally as "shair".