How is Cooper's age justified?

First of all, you have some parts wrong in your timeline and are missing others. So lets go through it again step by step:

1. The time taken to travel from Earth to the wormhole is 2yrs.

Check, aggregate = 2.

2. After that we don't know how much time passed on Earth while they were travelling the wormhole. Could be 10yrs judging from the advancement from the teenager to Casey Affleck.

There wasn't anything to suggest that there passed any time when passing the wormhole. Afterall it's a just a hole (and the movie depicts it as just that, albeit spherical, not some kind of black hole with unpredictably weird space-time effects) and its whole point is to connect two far away points by an immediate connection. They didn't travel any actual spacial distance through it. Also the first recorded message Cooper sees after getting up from the water planet is a young (non-Casey Affleck) Tom who says he just graduated from school (which would fit something like 2 years). Only then come the messages from the adult Tom.

So aggregate = 2.

3. Then, the time spent on watery planet being ~1-2 hour, assume 12yrs.

They're actually even more precise. When they get up, Romilly explicitly says that for him it was 23 years. So we're back near your own value, aggregate = 25.

4. Now, by the time they find Mann and Murph declares the death of Dr Brand, no appreciable time has elapsed as Murph is shown somewhat the same age as in her previous broadcast. So, no appreciable time change happens on that (Mann's) planet.

Check, there didn't pass much significant time, aggregate = 25.

And now you're missing something very significant. They make a little slingshot around Gargantua to get the necessary momentum for reaching Edmunds' planet. This brings them very close to the black hole, which we know causes significant time dilation. And in fact when they're around it, right before Cooper throws his ship into it, they joke about the effects of the time dilation causing another 51 years getting lost:

Cooper: This little manuever's gonna cost us 51 years.
Amelia: You don't sound so bad for pushing 120.

Just that now they didn't need to worry about it anymore (since at this point they assumed Plan A is dead anyway). So now we have aggregate = 76, which fits to Amelia's comment as well.

5. Then the time spent to the point where Cooper ejects into the blackhole is somewhat insignificant, given the chronology of events.
6. Now the time spent in the blackhole is again insignificant as Murph with whom he communicates through the wrist watch has still the same age, and for the paradox to work, she has to be his current daughter and not from some other timeline.

Murph's age is just insignificant here, since Cooper was moving through the tesseract and had access to a wealth of different times and saw her at different ages. The way he moved through space there, he actually moved through time. But Murph's age at this point is irrelevant, since it doesn't need to be congruent with his own, afterall he's already 76 years ahead due to the water planet and the black hole. It is Cooper and his relation to earth we're interested in.

7. After this, the next chronological event is Cooper waking up in the hospital and being told he is 124yrs old.

And in fact at some point after Cooper's return from Miller's planet Murph says in a message that she's now as old as he was when he left. Since she was 12 (I think to remember 10, but nevermind, doesn't make much of a difference), this would make him about ~35 when he left. So we have 124 - 35 - 76 = ~13 (+/-2 maybe) as the time that unexplicably vanished. This time we don't have an explanation for, since for Coop all of his experiences pretty much happened continuously. There could be different explanations for it:

• It could very well be some accumulated travel time between the different planets (afterall they had hibernation chambers and at some point they mentioned that it takes them months to reach Mann's planet) or maybe additional small bits of time dilation lost due to Gargantua's influence (afterall the time dilation should be smooth anyway, it's not like it just vanished if you're some safe distance, but I don't have my relativity formulas at hand right now, maybe it drops highly exponetially or whatever).
• It could have been additional time dilation that passed when he dropped into the black hole. He was getting nearer to it, and until he reached the event horizon and ended up is some crazy tesseract room, he was approaching a very real black hole, with very real time dilation effects, even if only for a short moment.
• It might have been time that passed while he was in the tesseract, in which we know weird time shit goes on.
• We also don't have to forget that he was conciously saved, put into the tesseract and later placed just outside the wormhole for convenient recovery. And all this by the effectively time-controlling "Bulk Beings" (or 5D superhumans from the future if you want), which might not be able to reverse time, but very well to stretch it, I guess. So they might just have deemed that to be the right time to put him there.

Given that a time difference of ~13 years isn't too big/significant (at least not as big as your own computed 60), I for one would settle on a combination of the first 2 explanations, as those are the most simple, natural, intuitive and unambiguous (even if also the most boring ;-)). But I admittedly don't know it either.

Cooper's age was between 35 and 44 when he left earth. As Murph's age was at least 35 by the time Cooper returned from planet Miller (10+2 years to Saturn +23 years on Miller), Cooper had to be older than 35 in order for Murph to be at her dad's age when leaving earth.

Further, Cooper was 124 upon returning, 120 upon entering the black hole, 69 (120-51) when Dr. Mann blown up , 46 (69-23) before entering Miller, 44 (46-2) before leaving earth. As time is needed to travel wormhole, to Miller, then to Mann's planet, etc. , 44 is the upper limit of Cooper's age when leaving.

Cooper was 35 - 38 years old when he left and Murph was 10 years old when her father left. 2 years for Saturn 23 years (Miller's planet) 51 years (Slingshot around Gargantua) 124 years old when Copper is found near Saturn So I would agree to say he has to be between the ages of 35-38 years old. I really want to go with 38 years old as I think there was a short time dilation when he entered back into the black hole.

I think it can be justified.

Romily says that 23 years have passed since they came back from Miller's planet - going by this you can revise your estimate in (2) to 23 years.

Now at the end we see Cooper falling as the Tesseract closes and he is later on rescued from Saturn (Movie's plot on Wikipedia confirms it). So assuming it took some time to search and bring him back and revive him - I think we might come close to the figure 124.

All times given in the movie seem exact multiples of 7 year/hour.

1. 23 years = 3 hours on Miller's planet x 7 year/hour + 2 years to Saturn
2. 51 years = (3 + 4 hours on Mann's planet) x 7 year/hour + 2 years to Saturn
3. 124 years = (3 + 4 + 5 hours in 5 dimensions) x 7 year/hour + 2 years to Saturn + 10 age of Murph + 28 age when Murph was born.