This is kind of tricky, as some books depict the same events from different points of view. Here's what the consensus seems to be:

             +--------------------+                      Backwards
             | "Survey: P.E.R.N." |                          ^
             +--------------------+                          |
             +-------------+                               Time
1st Pass->   | Dragonsdawn +----------------------+          |
             +-------------+ "The Dolphins' Bell" |          v
                           +----------------------+       Forwards
             +----------------------------+
             | "The Ford of Red Hanrahan" |
             +----------------------------+
             +-------------------+
             | "The Second Weyr" |
             +-------------------+
1st Int.->
             +--------------+
             | "Rescue Run" |
             +--------------+

             +-------------------+
             |  Red Star Rising  |
2nd Pass->   +-------------------+

             +------------------+
             | "Ever the Twain" |
             +------------------+
[...]
6th Pass->
                          +-----------+
             +------------+           |
             |  Moreta:   |           |
             | Dragonlady | Nerilka's |
             |  of Pern   |   Story   |
             +------------+           |
6th Int.->                |           |
                          +-----------+

[...]
8th Int->
                                                  +--------------+
                                                  |      The     |
                                                  | Masterharper |
                     +-----------+                |    of Pern   |
                     |           | +--------------+--------------+
  +----------------+ |           | |              |
  |"Runner of Pern"| |           | | Dragonflight |
  +----------------+ |           | |              |
9th Pass->           |           | |              |
                     |           | +--------------+
                     |           |               +--------------+
                     |           | +-------------+  Dragonsong  |
                     |           | |             +--------------+
                     |           | | Dragonquest | Dragonsinger |
                     |           | |             +--------------+
                     |           | +-------------+
                     |           +-------------+
                     |    The    |             +------------------+
                     | Renegades | Dragondrums | "The Impression" |
                     |  of Pern  |             +------------------+
                     |           +-------------+
                     |           | +---------------+
                     |           | | "The Smallest |
                     |           | |   Dragonboy"  |
                     |           | +---------------+
         +-----------+           |
         |           |           +----------------+
         | The White |           | "The Girl Who  |
         |  Dragon   |           | Heard Dragons" |
         |           |           +----------------+
         +-----------+           |
                     |           |
                     +-----------+
                     |  All the  |
         +-----------+   Weyrs   |
         |    The    |  of Pern  |
         |  Dolphins +-----------+
         |  of Pern  |
         +-----------+

                     +-----------+
                     | The Skies |
                     |  of Pern  |
                     +-----------+
                     
Notes:

Horizontally connected 'boxes' indicate closely connected (i.e. same events from different points of view) stories. Boxes connected vertically indicate that the following story takes place immediately after the previous one.

"Ever the Twain" does not have explicit indications of time-period, but the evidence suggests mid-to-late 2nd Pass or so.

Nerilka's Story starts 4 days before Moreta: Dragonlady of Pern.

"Runner of Pern" takes place in the spring just before the first Threadfall of the 9th Pass.

Dragonsong is shown to start previous to Dragonquest based on the timelines provided in Karen Fonstead's Atlas of Pern.

Dragonquest is shown to continue beyond the end of Dragonsinger based on the reports on Canth's healing which suggest that considerable time has elapsed since Canth's jump to the Red Star.

The White Dragon is shown to start before "The Girl Who Heard Dragons" since The Renegades of Pern indicates that the latter takes place in late autumn, while the former tends to suggest that the weather is just starting to turn cool.