Australian Mathematical Society journal rankings I apologize for a question that is not about mathematics, but I believe it is of interest to research mathematicians, and I believe there may be people on MathOverflow who can answer it objectively. If it is deemed unacceptable, I can survive.
For many years, I (and many others I know) have used a ranking of mathematics journals produced by the Australian Mathematical Society in 2009, formerly found here https://austms.org.au/Rankings/AustMS_final_ranked.html.
Without wishing to get into a debate on the usefulness or methodology of ranking journals, I found the list useful for judging what journals to submit papers to, and for justifying to deans or hiring committees the quality of journals that I or others (e.g. job, tenure applicants) have published in. I understand that it was getting out of date and I certainly did not agree with every grade there. But since it was made by mathematicians, rather than some trite formula, and since it used a simple A*/A/B/C grading scheme, it was solid and easy to reference and cite. For example, I planned to use it to help justify to deans an upcoming tenure decision.
It was also the top rated answer to this MO question about journal rankings. Unfortunately, the link above is now dead.

Question 1: Does anyone know if this ranking is permanently gone from the internet? If the society has "disavowed" it as incorrect or out of date? If they are revising it? Or if the link has simply changed?

I was able to find a "cached" version, so I still have access to the information. But I do not know how long this will be up, and it detracts from any semblance of authority if it is no longer hosted on a reputable website.
If this list is gone forever,

Question 2: Do people have suggestions for a replacement with similar features? (Made by a reputable institution, with input from mathematicians rather than a trite formula, and easy to explain to non-mathematicians.)

I understand that the second question has some overlap with the prior MO question linked above.
 A: This should perhaps be a comment rather than an answer, but I thought I should post it so that others can offer corrections or further detail.
One of my colleagues has sometimes justified his opinions/suggestions to me with references to the Scimago journal rankings in mathematics:
https://www.scimagojr.com/journalrank.php?area=2600&type=j
Unfortunately I don't know if these rankings carry the appropriate "weight" in the eyes of deans and similar creatures. (I also don't know about accuracy, but your post suggests that this is not really the main issue which you want to address; the ranking puts JAMS at number 3 and Annals at number 4, for what it's worth.)
There's a lot of finer-grained detail one can extract from this database, by selecting a particular country or a particular area of mathematics.

Some information which may be of interest to readers other than the OP
For background on this ranking or system of metrics, see
https://www.scimagojr.com/aboutus.php
The SJR number is described in technical detail
https://www.scimagojr.com/files/SJR2.pdf
and it appears to be a metric based on a version of the Google PageRank algorithm: some "alt text" on the webpage claims tha the SJR number

... expresses the average number of weighted citations received in the selected year by the documents published in the journal in the last three years.

A: The system officially used in Finland is Jufo. It has four grades in the ranking, from 0 (lowest) to 3 (highest). The funding of Finnish universities partly depends on the amount of publications in those journals, with coefficients per publication being 0.1 - 1 - 3 - 4 (i.e., a publication in a level 3 journal is worth 4 publications in a level 1 journal, and 40 publications in a level 0 one.)
The ranks are re-allocated every 5 years by a committee based on suggestions from the academics; also there are some constraints (if one journal goes up, some other has to go down). This naturally creates some distortions, e. g., a new strong journal will lag in ranking, which means that nobody has incentive to publish there, which means nobody will be strongly pushing to move it up the ranking etc. For example, "Forum of mathematics, Pi" is only level 1. But other than that, the ranking is reasonable.
A: There are several sources online that rank math journals by impact factor (and, this comes from a professor's webpage) or journal citation reports. However, it is important to realize that impact factor is a highly unstable metric, as discussed here.
Thomson Reuters has a list ranking by JCR, which appears to now be behind a paywall called InCites (though you might be able to access it through your library). If I remember correctly there was also an option to rank by impact factor.
The Institute for Scientific Information (ISI) is another source that maintains a database. And there's Scimago mentioned by Yemon. And you can look up impact factors over the years at bioxbio.com.
Another ranking by impact factor was SciJournal.org, but their website also appears to be down. A general way to solve the issue of disappearing website is the WayBack machine. For SciJournal, here is a recent snapshot from 2020. For the Australian list, here is a July, 2020 snapshot. In the same spirit as the Australian list, I am aware of a Chilean list that breaks journals into categories such as "Muy Buena," "Buena," and "aceptable" (I'm not sure if this is actually the third category). I've heard that this breakdown is not super well-regarded.
Lastly, an alternative to impact factor, that I've read about but have not yet looked into, is scite.
A: I think all the other questions have been answered. The reason the link you posted is now dead is that the Australian Mathematical Society updated its (very old) website recently. Yes, you can find this link on web.archive.org. For what it's worth, your link is the 2008 list. The 2010 list, the final edition of the ERA rankings, can be found here http://www-users.math.umn.edu/~arnold//math-journal-ratings/ - this is "only" 10 years out of date rather than 12.
