There is no way to truly force this pronunciation in English.
In English, we just don't pronounce the /h/ sound at the end of syllables. Because it is not a part of our phonological grammar, it can be difficult for a native English speaker to articulate the sound, or even perceive the sound at all, in that context. So, even if you pronounced it correctly and asked the native English speaker to repeat after you, they might still leave out the /h/ sound.
Since there is no context in which an English speaker pronounces /h/ at the end of a syllable, there is no spelling convention that indicates it should be done to someone who is unfamiliar with Farsi.
It is similar to trying to write something in katakana that will make a native Japanese speaker pronounce "cat" as we do in English. Japanese speakers have the /t/ sound, but it can't occur at the end of a syllable, so the closest approximation would be "kato" (or "katto" but let's keep it simple).
There are two spellings available to you, each one sacrificing one feature in favor of another.
- The standard spelling "Tehran" maintains the two-syllable prosodic form and indicates the "h" for those who are familiar with Farsi Latinization and phonology. But it will not cause an average speaker to pronounce the "h".
- The alternate spelling of "Teheran" (which was mentioned in the comments) puts the "h" in a context where it can be pronounced (at the beginning of a syllable — "he"), but in order to do so, adds a vowel and therefore another syllable. This is called epenthesis and is also how Japanese (among many others) repair unpronounceable clusters. The disadvantage is that you now have three syllables instead of two; also, you still aren't guaranteed to get pronunciation of the /h/ sound — between vowels, an "h" in an unstressed syllable often goes unpronounced in English.
So which pronunciation is standard for the [ʊ] sound? Rounded or unrounded?
Certainly there is some rounding, but because roundedness is not phonemic in this position, there is also considerable variation in how much of it actually occurs in any given word and speaker.
For example, you will find that it is generally somewhat more rounded in pull and full than it is in put and foot respectively. That’s because having an r or an l right next to it rounds it off a bit — which is why it is a bit more rounded in root and rook than it is foot or cook. Same with rookie versus cookie, where the first version is a bit more rounded than the second. And of course, a w helps: compare how wool is even more rounded than full, and also moreso that wood.
I believe English has no words with [ʊw], as that seems redundant. However, it can occur in phrases, especially in some dialects, where something like I knew it full-well may approach that.
However, it is still perceived as the very same phoneme in all those words and cases I’ve just listed above.
Correction — or not
I said that I thought English had no words with [ʊw] in them. And at the end of the day, I still believe that. However, I have discovered that grepping the OED yields the apparent existence-proof counterexample of Rauwiloid, which means:
A proprietary name for a hypotensive preparation containing a number of alkaloids extracted from Rauvolfia serpentina.
You also have compound words whose first element ends in [aʊ] (rather than [aw], as it is sometimes spelled) connecting to something that begins with [w], and which have in effect a “double w” in them, you expand the list to include such things as:
bow-wow, powwow, skeow-ways, wow-wow
Finally, if you consider the sound in words like no and micro to be
an [oʊ] diphthong rather than [ow], then you get all these, most of which were originally compounds of some sort:
froward, frowardly, frowardness, glow-worm, Holloway,
hollowwort, Howeitat, Khowar, meadow-wink, microwave, microweld,
Moldo-Wallachian, nowise, Oldowan, Parowax, powan,
shalloway, slow-worm, swallowwort, werowance,
yellow-wood, yeowoman.
For example, yeowoman theoretically yields /ˈjoʊwʊmən/, at least in North America. Still, there is a reasonably convincing argument to be made that that one is better written as simply /ˈjowʊmən/.
Slightly less uncommon is nowise, which is a compound of one word ending in a diphthong connected to another starting with a triphthong, so /ˈnoʊˌwaɪz/.
But I am still highly dubious of the existence of [ʊw], because I think it fuses into the semi-consonantal glide, [w]. After all, nowise and no eyes are homophonic, so I think this idea of [ʊw] is very hard to justify, and so I stand by my initial statement.
Even towel is usually pronounced with just one syllable, /taʊl/, thereby rhyming with cowl /kaʊl/. Even with folks who work very hard to put two syllables into that, with /ˈtaʊ.wəl/, I submit that you could write that /ˈtawːəl/ and avoid the whole controversy of whether a semi-vowel/semi-consonant/off-glide is really /ʊ/ or really /w/. However you write it, it seems like the same sound to me, such that bisyllabic towel just has a geminate [w]: /ˈtaw.wəl/.
Best Answer
Firstly, native English speakers do not add an extra n after the /ŋ/ in the word singer, though some do have the same issue as you with having difficulty producing /ŋ/ in the middle of words like singer and singing.
The "ng" sound in medial and final word position can be challenging for native Russian speakers. What's happening is that /ŋ/ is a continuant sound, and if you release the tongue from the sealed position for the /ŋ/ while you are still producing airflow, you will make a /g/ or /k/ sound because the release of the built-up air produces the sound.
The way to avoid this problem is to begin to shape the vowel for the "-er" before releasing the /ŋ/ tongue position, and to release the tongue gently into the vowel. If no air is allowed to build up, the plosive/stop g sound will not be produced.
You can hear the pronunciation of singer in this video: https://youtu.be/c-3HtmE5muY and get more information about the /ŋ/ phoneme in American English in this video: https://youtu.be/-DZ5GICTHVU
I will be making a more specific video to help with words with "-nger" and "-inging" in the future, as I have heard from many Russian and other non-native speakers that these are particularly difficult to make without the "g" sound intruding. I'll add it to this post as an edit when it's complete.