Tomb/Ebon - 6
Masts/Asura - 4
Yeti/Lair - 2
DC - 3 (4 Weekend)
CS/JSY - 2
Jadestone Event - 1
Assuming these basic ones, you can get 18 on a Weekday, and 19 on a Weekend Day.
Since the event runs until February 8th, we can assume February 7th is the last day to get coins, since maintenance occurs Tuesday night into Wednesday.
12 Weekdays (18 coins ea, 216)
9 Weekends (19 coins ea, 171)
This gives 389 Coins for an alternate character. This is of course, skipping Nexus, Necropolis, and Gloomdross.
On some days, Necropolis & Nexus & Gloomdross are INCLUDED in the daily rotation - especially Nexus quite often.
This means that in addition to 389 coins, you will have done at least 4 runs of Nexus and 2 runs of Necropolis due to the DC rotation.
This puts an alt character at 400+ coins, enough for the 35 AP gem + transmutation.
You can do this on 3 characters for three 40 AP gems.
If you want the outfit, oil, or other goodies you can look to the daily dash (10 bags, 20 coins per completion, Jadestone box bonus procs) and the Hongmoon store for additional coins.
All in all, this event should be very doable while skipping the long and unnecessary dungeons.