Low voltage AC relay
What are you even trying to do in that circuit?

C1 will limit the current, potentially preventing a sufficiently strong magnetic field to develop in the relay coil.

Then D1 prevents half of the AC current from flowing through the relay coil further weakening it again.

But none of that matters because you have a short-circuit across the relay coil which routes all current away from the relay coil through the short so no current flows through the relay at all.

If you are trying to make AC-DC, that is not how you do it. But changing AC-DC won't fix your problem anyways because it's a relay with an AC coil to begin with.

Relays have a rating for the primary contact which is what they can control. Then they have a rating for the coil which is is used to control the relay. You did not specify what was 6VAC was for.

But that also doesn't matter because your appliance and relay coil are connected incorrectly. Why is your relay coil in series with your appliance? That doesn't make sense.

Normally the relay coil would need to be in parallel with the appliance to do what you want to do. But that doesn't work if your relay coil doesn't also run off the same voltage as your appliance which is what what? 120VAC or 240VAC? What does your relay coil run off of? I don't know, you never actually told us what the relay coil runs off. You just said it was 6VAC but that could mean two things. If the relay coil is 6VAC it won't work and if the primary contacts are 6VAC then the relay coil is probably not 120VAC/240VAC.

You say your timer circuit is using 6VAC, but that kind of doesn't matter if it's supposed to be acting like a switch. If the timer is acting as a switch, it's doing just that: being a switch. It's not supplying its own power to the load. It's just acting as a gatekeeper between the load and power supply for the load, whatever they may be.

The timer circuit is controlling your appliance and I bet your appliance doesn't run off 6VAC. So why do you think the relay coil needs to?

You have not actually labelled any voltages in your schematic either so I can't even tell you how far off base you might be in your misinterpretations of what voltages are required where.

From what I have seen, you need to learn some basic circuits before attempting anything because there is so much wrong here I can't even tell you how to fix it. Information, particularly ratings of everything in your circuit, is also lacking.