I) Specifically about covariance:
1) The covariance tag is supposed to cover whatever-notion-the-physical-system-in-the-question-is-covariant-under, typically relativistic covariance, but also more abstractly, e.g., contravariant and covariant tensors not necessarily in the context of relativity.
All other uses of the covariance tag than the above are wrong.
2) Covariant derivatives in differential geometry should be tagged differential-geometry or gauge-invariance and perhaps differentiation. (The covariance tag could apply here if the main topic of the question is point 1.)
3) Gauge Covariant derivatives should be tagged gauge-invariance and perhaps gauge-theory and differentiation.
4) Covector, bivector, differential forms, etc, should typically be tagged with differential-geometry or tensors.
5) Statistical covariance, average, etc, should be tagged with statistics (which in turn should only be used for statistics in the mathematical sense. E.g. Fermi-Dirac statistics etc. go under quantum-statistics and perhaps statistical-mechanics, while the spin-statistics tag is ideally reserved for issues related to the spin-statistics theorem).
II) More generally, the issue of tagging is non-trivial and difficult to make perfect. Since the system doesn't know which tags are close, and which tags are far apart in tag space (the metric is the discrete metric), it is often better to have broad tags with simple rules rather than specific tags that nobody else will use consistently or have heard about. In plain English: it might be better to compromise and either (i) tag dromedary questions with the camel tag rather than introducing a new dromedary tag with the consequence that the system will no longer recognize that posts with dromedary and camel are likely very similar; or (ii) make dromedary a synonym of the camel tag, with the consequence that questions tagged with dromedary would automatically be retagged as camel by the system, even if experts of dromedaries would strongly object to this.
There will likely continue to be tags that cause various problems. E.g. the tags mathematical-physics and specific-reference are often applied wrongly.
Non-descriptive tags, such as, e.g. general-physics, differential-equations, equations-of-motion, etc, should be avoided as they serve little purpose. (Many questions on Phys.SE involve differential equations and equations of motion.)
An ambiguous tag, such as, e.g. space should either be replaced by geometry, spacetime, vacuum, space-travel, etc, depending on context. Or the proper use of an ambiguous tag should be spelled out in the corresponding tag wiki. E.g. use of the distributions tag is explained in its tag wiki.
And so forth.