The important part: Only one of each of these items can ever be built per team per game. If they are sold, they're gone. Also, each of these items should build into (at least) 2 legendary-tier items:

1) An item with Tenacity. The only other item that offers Tenacity should be Merc Treads (if even that).
2) An item that is, stat-wise, of slightly above-average gold efficiency, but below-average slot efficiency, and also offers a useful active ability.
(Additional items should also be cost-efficient and have interesting actives.)

Both items should be viable end-game picks, since they're not going to make frequent appearances.

Impact: Supports get their income quicker and can still do their job effectively while doing so thanks to the variety of items offered. Also, early, aggressive play is rewarded, since a kill puts you half-way towards one of these items. Aggression is especially rewarded for supports, who are likely to buy 3-4 of these items. That said, because of the one-per-team restriction, buying multiples of these items when *not* playing Support will almost certainly gimp your support and make late-game effectively a 4v5, or force someone else to share farm with your support and making your team weaker, overall. It's also impractical to buy multiple items on non-supports and be effective because the stats on these items are highly varied. An ADC and an APC really only each want one of these items, while a bruiser or tank might want 2. Supports that need survivability and utility will like collecting them, however, not only because you need a lot of different stats to cover those two roles, but also because the items these build into will improve their utility even further.

First, the existing gp10 items:

Philosopher's Stone:
Bead of Rejuvenation (250g) + Faerie Charm (180g) + Recipe (170g) = 600g
+12 health/5
+5 mana/5

Avarice Blade:
Dagger (420g) + Recipe (180g) = 600g
+25% Attack Speed

Heart of Gold:
Ruby Crystal (475g) + Recipe (125g) = 600g
+225 Health

Kage's Lucky Pick:
Amplifying Tome (435g) + Recipe (165g) = 600g
+25 AP

Next, existing items that should be gp10's:

Mana Manipulator:
Meki Pendant (390g) + Recipe (210g) = 600g
+8 mana/5 aura

Emblem of Valor:
Rejuvenation Bead (250g) + Cloth Armor (300g) + Recipe (50g) = 600g
+8 health/5 aura
+18 armor

Also, ideas for a new gp10's:

Enchanted Sapphire:
Sapphire Crystal (400g) + Recipe (200g) = 600g
+350 mana

Starmantle:
Null-Magic Mantle (400g) + Recipe (200g) = 600g
+35 Magic Resist

In addition to listed stats, these items all, obviously, increase gp10 income by 5.

EDIT: Changed the order because nobody is commenting on the important part, making me think they're just not even reading it and looking at these like normal items.

I would hope that on a feedback forum, people would actually give feedback.

No... now that I've gotten that out of the way. I think they should make avarice boots
Avarice boots:
built from: boots
cost to upgrade: 200
grant: movement speed 2, 5 gold per 10

Sorry, doing homework and tired.

1. Changing Avarice Blade in particular doesn't seem like a good idea. I know that crit is the weakest offensive stat to put on a gp10 item, but it should remain as this weaker stat. Gp10 items are meant to be an investment for later income or wards that include some risk to the champion's effectiveness. Since ad champions--particularly ranged ad carries--get the most benefit from building items do to their item-dependency, I don't think that it is wise to enhance the item, Particularly considering that the upgrade you are suggesting for it has 109% cost-efficiency for a type of item that is specifically supposed to be cost-inefficient.

2. Most of the other price cut suggestions you suggested also include cost reductions that gp10 items should not get.

3. It seems that you are trying to put the gp10 bonus on too many base items that should not get it.

4. I like the two new ideas, but unfortunately the current gp10 items already cover all of the bases (sustain, defense, offense) and there is no need for redundant items.

GP10 should never be added to an item that you do not have to sell or upgrade later. This means no gp10 on boots.

I'm not sure you got to the important part, Axes. I'm suggesting a new mechanic that, IMO, would address most of your concerns, and brings into play another balance consideration for these items: if I buy Philo Stone as an AD top, then I'm potentially denying my Jungler or Support an extremely useful gp10 item that they could likely make better use of than myself, or that they need more than I do.

Also, there are balance considerations for end-game. I noted that these aren't supposed to be the best end-game stat-sticks, but rather provide utility as opposed to raw power, and that even if sold, they're gone for the rest of the team. As such, ADC's that want stat sticks probably shouldn't buy any of these items for reasons beyond their early-game cost-effectiveness.

Bad idea. You nerf a item used by many, and buff by a lot all others. Then, will be even easiest to capitalize.

You can't try to "balance" an item by putting restrictions on who can buy it either. This game is not "balanced" in that way.