The timeline for the series Road to Avonlea between 1903 and 1912.

Season One

Spring/Summer 1903
1.1: The Journey Begins-- It is generally agreed that the series started in 1903, probably in the summer. 
1.2: The Story Girl Earns Her Name 
1.3: The Quarantine at Alexander Abraham's 
1.4: The Materializing of Duncan McTavish 
1.5: Old Lady Lloyd 
1.6: Proof of the Pudding 
1.7: Conversions 

Fall/Winter 1903-1904
1.8: Aunt Abigail's Beau -- An advertisement for the infamous auction is dated Tuesday November 9 (This date in 1903 actually falls on a Monday).
1.9: Malcolm and the Baby 
1.10: Felicity's Challenge—The Harvest ball 
1.11: The Witch of Avonlea 
1.12: The Hope Chest of Arabella King --’ the Avonlea Chronicle was dated Tuesday December 12, 1902. This is likely a typo and it's probably December 1903. (It's possible that the series was originally intended to begin in 1902 in pre-production, and then later bumped up to 1903 for some reason)
1.13: Nothing Endures But Change 

Season Two

Summer/Fall 1904
2.1: Sara's Homecoming—Takes place around Dominion Day on July 1st. This means it’s June/July 1904.
2.2: How Kissing Was Discovered -- The date in Felicity’s diary is June 13. (1904). Felicity says that she is 13 and ¾. 
2.3: Aunt Hetty's Ordeal -- The date of the Avonlea Chronicle is September 14, 1904. 
2.4: Of Corsets and Secrets and True True Love
2.5: Old Quarrels, Old Love 
2.6: May the Best Man Win 
2.7: Family Rivalry

Fall/Winter 1904-1905
2.8: Sea Ghost 
2.9: All That Glitters 
2.10: Dreamer of Dreams 
2.11: It's Just a Stage 
2.12: A Mother's Love 
2.13: Misfits and Miracles—Daniel King is born. 

Season Three

Spring/Summer 1905
3.1: The Ties That Bind -- Season Three probably starts in 1905. Jasper proposed to Olivia around late summer/early fall 1904, and it’s likely they are married the following summer. 
3.2: But When She Was Bad...She Was Horrid (part 1) 
3.3: But When She Was Bad...She Was Horrid (part 2) 

Summer/Fall 1905
3.4: Felix and Blackie 
3.5: Another Point of View 
3.6: Aunt Janet Rebels --Felix mentions that Felicity is 15 years old. Felicity turned 14 in Fall 1904, so it’s probably 1905. 

Fall/Winter 1905-1906
3.7: A Dark and Stormy Night 
3.8: Friends and Relations 
3.9: Vows of Silence 
3.10: After the Honeymoon 
3.11: High Society 
3.12: The Calamitous Courting of Hetty King 
3.13: Old Friends, Old Wounds 

Season Four

There might be a one year gap here as previously stated IF season four starts in 1907. 

Spring/Summer 1906 (or 1907)?
4.1: Tug of War—Olivia has a baby, but there is no mention of her being pregnant last season. Mag Ruffman described researching child birth for this episode and having a short time to do so. It’s likely this wasn’t decided until this season. 
4.2: The Lady and the Blade

Fall/Winter 1906-1907 (or 1907-1908)?
4.3: Incident at Vernon River—Felix’s birthday 
4.4: Boys Will Be Boys 
4.5: Moving On 
4.6: Evelyn 
4.7: The Dinner 

Hannikan has suggested that the missing year/time gap may also appear here, pointing out that 'The Dinner' and FPB are very close together in terms of subject matter. 

4.8: Heirs and Graces—An advertisement on the bulletin board is dated November 1907. Thanks to Hannikan for pointing out the Victorian typeface for sevens.
4.9: Hearts and Flowers—February 1908 
4.10: Felicity's Perfect Beau

Based on the date from Heirs and Graces, a few things become clearer. The missing time of season four likely does not appear here, as there is now strong continuity from Heirs and Graces into the fifth season. We now know that the Gus and Arthur rivalry occurs in early 1908.

Winter 1908
4.11: The Disappearance Winter 1908. When Felix asks about the assignment of where they will be in the next ten years, Gus says 1918, which suggests that it’s winter 1908. This means that up to this point--(1) either most of 1907 is missing, (2) Season Four takes place in 1907, or (3) Season Four spans 1906-1908 with only one summer featured. 
4.12: Home Movie 
4.13: Hearth and Home 

Season Five

Spring/Summer 1908
5.1: Fathers and Sons – Following the winter of 1908, it’s presumably spring/summer 1908 when season five rolls around:
5.2: Memento Mori
5.3: Modern Times

Fall/Winter 1908-1909
5.4: A Friend in Need
5.5: Stranger in the Night—The Avonlea Chronicle newspaper is dated 1908. The day is listed as the 14th but the month is not visible.  Judging by the orange and yellow leaves, this episode takes place in the Fall  (A property auction notice is posted on the bulletin board for November 13, 1907. This must be erroneous however since it is clearly 1908. The advertisement was likely repurposed from an earlier episode).
5.6: The Great Race—A sign for the race indicates that it’s October 1908. A prop sign from the series indicates that the race occurred on October 4, 1908. 
5.7: Someone to Believe In 
5.8: Strictly Melodrama
5.9: Thursday's Child
5.10: Best Laid Plans 
5.11: Otherwise Engaged
5.12: Enter Prince Charming
5.13: The Minister's Wife

Season Six

Summer/Fall 1909
6.1: The Return of Gus Pike
6.2: Lonely Hearts
6.3: Christmas in June—A letter addressed to the King family was dated June 19, 1909. 
6.4: Comings and Goings—Sara was in Montreal for six months. 
6.5: The Trouble with Davey
6.6: Great Expectations

Fall/Winter 1909-1910
6.7: A Fox Tale
6.8: Fools and Kings—Gurney comments that Felix is nearly 16. 
6.9: The More Things Change 
6.10: Home Is Where the Heart Is
6.11: What a Tangled Web We Weave
6.12: A Time To Every Purpose --A newspaper carrying the article 'Local Girl Enters Brave New World of Medicine' is dated February 9, 1910 (could have been January, but looked like February.)
6.13: Homecoming

Season Seven

The time gap between February+/- 1910 and Summer 1911, so roughly a year and 1/2 between seasons.

Summer/Fall 1911
7.1: Out of the Ashes—The ‘Avonlea Foundling Home’ sign indicates that it was established in 1911. 
7.2: Love May Be Blind...but the Neighbours Ain't
7.3: Davey and the Mermaid
7.4: Woman of Importance—Izzy is nearly 16. 
7.5: Secrets and Sacrifices—Lucky is 7 and a half years old. 

Fall/Winter – 1911?
7.6: King of the Great White Way 
7.7: Total Eclipse
7.8: Ah...Sweet Mystery of Life 
7.9: From Away
7.10: After the Ball is Over—Eliza Ward turns 90. Lucky turns 8 in this episode. Lucky was a baby in 1903 and 8 years later would make the current year 1911. 

* There is a 1+ year gap here IF the series ends in 1913. The original RTA website stated that the seventh season is around 9 months from the "brink" of WW1, which means the series ends in 1913. However, there are two references in HCMK for a two year span between the end of the 7th season and HCMK. This would mean the series ends in 1912. Therefore, there are two contradictory years mentioned when the series ends.

Spring/Summer 1912 OR 1913?
7.11: Return to Me—Spring/Summer 
7.12: The Last Hurrah 
7.13: So Dear to My Heart