I fee like this has always been an ongoing argument of whether to take coin or spellthief's on Janna. I personally preferred spellthief's because of the AP and the better gold income, but with the recent buffs to coin that are hitting the PBE, and this is if these buffs happen, I think coin might actually be just as good as spellthief's now.
To start with, here's some math:
1 minion wave = 6 minions
Every 3rd minion wave = 7 minions
1 minion wave per 30 seconds.
12*3 = 36 gold per minute
57 gold per 1.5 min
Upgrade to medallion:
12*4 = 48 + 12 (2 per 10) = 60 gold per minute
68 +18 = 86 gold per 1.5
1 charge per 10 seconds - store up to three
2 per 10
42 gold per minute
63 gold per 1.5 minutes
Upgrade to Frostfang:
72 gold per minute
108 gold per 1.5
As you can see, Spellthief's does net you more gold, but that is _only_ if you get every single proc of the passive. And for a support like Janna, unless you're really dominating lane, I feel like you _are_ going to miss a few procs and so the gold difference may end up being not as big. (Coin buff would give you 11 more gold every 1.5 minutes than before. While you might miss a few minions in lane, the difference shouldn't be _as_ big, I think.)
But this is all very situational so that being said, let's look at the pros and cons of both items disregarding the lane matchup.
Coin and Spellthief's both have 25% mana regen. Spellthief's, however, grants you the extra gold per 10 that coin does not offer until Medallion. Spellthief's also gives 5 ap (which is minimal, but everything counts early game) and it's passive does extra damage per proc.
Coin upgrades to Medallion which, with the buffs, will give you 50% mana regen, 25% health regen, 10 ms and gold per 10. Frostfang gives 5 more ap and 50% mana regen. The passive does 5 more damage than spellthief's when proc'ed. As Janna, I'm not sure you really need that health regen and the ms is nice, but not _really_ needed either (though it does synergize well with her because of her w). Minion deaths will give you extra health (60 per minion wave upped from 30) which is a plus for healing back minimal amounts of poke.
What I do really want to talk about is the final upgrade.
Frost Queen's Claim, as I've found, is rarely a prioritized item. I build it if I have extra money and want some ap for my shield. It has a nice active, an 80% slow for 2 seconds + some damage, but I personally am not a huge fan of it. The projectile too slow and I find it's effects not as satisfying as I want them to be. It doesn't give any more mana regen than Frostfang and the passive damage of tribute stays the same, so there's really not much of a reason to upgrade this item unless I really need it.
Tailsman grants much more regen, both 100% health and mana and +20 ms. Janna already has a built in MS steroid with her w, so I actually think this extra MS synergizes pretty well with her. She doesn't _need_ it, but I think it's very much a plus for her. The biggest thing though is the fact that the active is now up every 40 seconds for a 40% MS buff to all nearby allies, as opposed to an AoE skillshot slow for 2 seconds which is only up ever 60 seconds. Tailsman has always had the better active for Janna, but spellthief's was a much better gold income item and it was somewhat inefficient to sell spellthief's to buy tailsman.
Spellthief's was always the more aggressive support item because you do more damage poking and you gain gold that way. Coin was for more passive supports, but it was a really weak gold gen item. But now with the mana regen buffs and the buffs on Coin's gold gen, for a support like Janna where you can poke but also sit back and let your adc farm, could coin be a "better" start now?
So, after all this, opinions? New coin or spellthief's?
Applause to anyone who survived my long rambling mess.