What you are describing is an annular eclipse, where the moon is not quite as big (visually) as the star it eclipses.
This is not possible.
First off. An eclipse is a localized phenomenon. The parallax of being in different places on the planet looking at the star and the moon will give them different relative positions. To eliminate this problem, the "moon" would have to be closer to the star than to the planet and almost as big as the star.
A global total solar eclipse is possible, if you are on a moon being eclipsed by the planet it orbits. The planet is bigger than the moon and casts a bigger shadow that the moon can fit entirely within. This won't give you the ring of light that an annular eclipse does though. If the planet has an atmosphere, then you might be able to see it lit up like a ring shaped sunset. That's why the moon is red when eclipsed by Earth.
Making that permanent though isn't going to work. Tidal locking is about the rotation of a body about its axis, not its movement though its orbit. The moon is locked to Earth which means we see the same face of.
You can't make the orbit of the moon around the planet the same duration as the orbit of the planet around its star (which is what you are probably trying to get at with your double tide lock idea) The moon would be so far away, it wouldn't be in orbit around the planet any more and certainly wouldn't be close enough to cause an annular eclipse.
To get something at a fixed position with respect to the star would require positioning at a Lagrange point. Either L1 or L2. These can be thought of as "orbits with periods equal to the orbit of the planet" but it's a bit more complicated and only two points work, not the whole orbit. Those points are directly in line with the star though so that might seem it would work.
L1 is between the planet and its star. If something were that big enough to block the star, you'd get a permanent eclipse, until it drifted away which would eventually happen as L1 is unstable.
L2 is on the far side of the planet so you might be able to get a planetoid (not exactly a moon or a planet) to sit there, although it's again unstable so the planetoid would drift away from the point eventually.
Earth Sun L1 and L2 are about $1.5\times10^6\rm{\,km}$ from Earth. When it's causing an annular eclipse, the Moon is about $4.0\times10^5\,\rm{km}$ from Earth. Moving the moon out that far would reduce it's angular size by a factor of $3.75$ so we'd have to scale up its radius by the same amount to keep it visually the same. That would make it slightly larger than Earth! Even if it weren't for the instability of L1, it would need an incredibly low density to avoid disrupting the whole system.
Conversely you could do something like put Jupiter at $0.93\,\rm{AU}$ then put Earth at Jupiter-Sun L2 ($1\,\rm{AU}$ from the sun), Jupiter would be about 50 arc minutes in radius (if I did the math right). This would be a bit less than twice the angular size of the sun at that distance. You might see a bit of light around the edges of Jupiter diffracting through its atmosphere. This would be subject to parallax variation, but not as much as with an annular eclipse.
You have the basic problem of stability though. Earth might stay at L2 for a little while, but it would drift away without something holding it in place. It would end up as a moon of Jupiter, crashing into Jupiter or being flung out of the solar system.