When playing 2v2, can you share gold for each other's recycle cost?

No, you cannot share resources or use your teammate's resources to pay for your own costs in 2v2.

According to Rule 484.8.c, "Control is not shared" in 2v2. Each player maintains their own Rune Pool and acts as an individual controller of their own cards and resources. While teammates can communicate and coordinate, they cannot draw from each other's Rune Pools or use each other's units/gear to pay costs unless a specific card effect explicitly allows it.

Regarding "Gold" specifically, if you are referring to Gold gear tokens: they provide Power to your own Rune Pool when their ability is activated (as clarified in RiftJudge FAQ #9133). Since you only control your own gear, you can only trigger the ability of the Gold gear tokens that you control.