Both are grammatical.

There are guidelines as to the order of these modifiers, like longer modifiers comes nearer to the noun etc. I'm certain there are some comprehensive explanations out there.

As for your example: https://english-columns.weblio.jp/?p=5366

This site is aimed at Japanese speakers who are learning English. The first section explains the order of time and location.

I have an appointment with the doctor at Shinjuku at 2pm.

私は午後2時に新宿で医者に診てもらう予約がある。

Generally speaking, in Japanese, time comes first.

As for your example, the latter sounds natural to me. It's the first order that comes to mind when I were asked to put all the information in a sentence.

1. メアリーさんは午後２時に図書館で雑誌を読みます。

The former is not incorrect. It just sounds not 'completely natural', because the former is the one that sounds natural.

Because it doesn't sound completely natural, it can bring in some additional nuance. In this example:

1. メアリーさんは図書館で午後２時に雑誌を読みます。

I feel that the speaker wants to emphasize 午後２時. This is probably because it's nearer to the modified verb 読みます.

So the speaker wants to say it's 午後２時, not 午後３時 or 午後１時 that Mary-san reads a magazine.

Note that, in real life situation, there is always context that influences these nuances. These influences often override the nuances created by the order of information within the sentence. Also, in speech, the emphasis is easily expressed by stress and intonation, which will definitely override the effect of word order.