Chronological order:
1835: Mortimer Montgomery (Monty's father)
1839: Martha Montgomery (Monty's mother)
1847: Count Olaf XVIII (Olaf's father)
1855: Chas Snicket (Snickets' grandfather)
1855: Evadne Snicket (Snickets' grandmother)
1855: Jeffrey "Jeff" Horowitz (Esme's father)
1864: Tatiana (Olaf's mother)
1867: Lucy Montgomery (Monty's sister)
1869: Gigi Genevieve Horowitz (Esme's mother)
1869: Arthur Connolly (Josephine's father)
1869: Gladys Connolly (Josephine's mother)
1871: Walter Strauss (Snickets' uncle)
1874: Jenna Strauss
1876: David Snicket (Snickets' father)
1876: Penny Strauss (Snickets' mother)
1879: Garrett Stoppard (Charles' father)
1882: 23rd March, Monty Montgomery.
1883: Kevin Remora
1883: Victoria "Vicki" Bass
1885: 3rd May, Jayne "Jai" Rutland (Monty's girlfriend)
1885: 3rd May, Niles Nero
1886: Abigail "Gail" Snicket (Snickets' aunt)
1888: Hugo Victor
1889: Tom "Sir" Uttamatomakkin
1890: Fatima Romanov (Fernald & Fiona's mother)
1891: 29th December, Count Olaf XIX
1891: Kevin Copperfield (Ambidextrous Kevin)
1891: Maurice Pitaccatio (Bald Man)
1891: Anthony "Tony" Bernstein (Person of Indetermined Gender)
1891: Margaret "Peggy" White (White Faced Woman #1)
1891: Susan "Sue" White (White Faced Woman #2)
1891: Rachel "Rae" White (White Faced Woman #3)
1892: Julien Horowitz (Esme's brother)
1893: Phil Timmins (Optimistic Phil)
1894: Livius (Olaf's brother)
1895: Derek Connolly (Jo's brother)
1895: Bruce Spats (Carmelita's uncle)
1896: Arnaud Horowitz (Esme's brother)
1898: Gerard Horowitz (Esme's brother)
1898: Lucia Denouement (Denouements' sister)
1899: 21st November, Josephine Connolly.
1899: Isaac Anwhistle.
1900: January, Rene Horowitz (Esme's brother)
1901: 18th April, Esme Horowitz.
1901: Sarah Lugosi (Quagmires' mother)
1901: Malachi Quagmire (Quagmires' father)
1901: Andrew Squalor (Jerome's brother)
1902: 26th April, Kit Snicket
1902: 26th April, Jacques Snicket
1902: Pollyanna "Polly" Poe.
1903: 28th Feburary, Lemony Snicket.
1903: Beatrice Baudelaire
1903: Bertrand Baudelaire
1903: 6th October, Rheanique "R" Winnipeg
1903: Edwin Poe (Mr. Poe's brother)
1903: Stephin Merritt
1903: Damarnie Spats (Carmelita's father)
1903: Naomi Bleek (Carmelita's mother)
1904: Colin Connolly (Jo's brother)
1904: 27th January, Jerome Squalor
1904: 26th April, Frank Denouement.
1904: 26th April, Ernest Denouement.
1904: 26th April, Dewey Denouement.
1904: Lysandra Squalor (Jerome's wife)
1906: 28th October, Fernald Smith.
1907: Arthur Poe.
1909: 3rd August, Charles Stoppard.
1909: Georgina Orwell.
1910: May, Colette DuPont.
1915: Eleanora Poe.
1918: Joshua "Josh" Snicket (Kit & Olaf's son)
1918: Faith Harlow (Phil's girlfriend)
1919: Anastasia Wilde (Olaf's daughter)
1920: Joel Fisher (Esme's boyfriend)
1921: Angelina Uttamatomakkin (Sir's daughter)
1923: Fiona Smith
1924: Violet Baudelaire
1925: Isadora Quagmire
1925: Duncan Quagmire
1925: Quigley Quagmire
1926: Klaus Baudelaire
1927: Albert "Bertie" Poe.
1928: 1st July, Carmelita Spats.
1929: Emily Uttamatomakkin (Sir's daughter)
1929: Edgar "Eddie" Poe.
1935: Miriam (Faith's daughter)
1937: Sunny Baudelaire
1938: Antoinette (Faith's daughter)
1938: September, ASOUE begins.
1939: 15th July, Beatrice Baudelaire II
1939: WWII begins.
1939: 9th November, Moses Horowitz (Esme & Olaf's son)
1940: April, Bella Poe (Mr. Poe's daughter)
1941: Ethan Fisher (Esme & Joel's son)
1944: 10th October, Gerald Andersen (Sir & Charles' adopted son)
1946: Pierre DuPont (Colette's son)
1946: Alistair Poe (Albert's son)
1947: Patience Fisher (Esme & Joel's daughter)
1947: William Squalor (Jerome & Lysandra's son)
1949: Duncan Baudelaire (Klaus' son)
1951: Quigley Baudelaire (Klaus' son)
1954: Fiona Baudelaire (Klaus' daughter)
1955: Larson (Colette & Fernald's adopted son)
1957: Beauty Croft (Violet's daughter)
1958: Hamish Poe (Edgar's son)
1966: Wayne (Gerald's son)
1969: Alan Poe (Alistair's son)
1969: Martin (Gerald's son)
1971: Aaron Poe (Alistair's son)
1975: Anna (Gerald's daughter)
1975: Rowan (Bella's son)
1991: Adam Poe (Alan's son)
1992: Samantha (Gerald's daughter)
1994: Harry (Gerald's son)
1996: Lucille Poe (Hamish's son)
1997: AJ Poe (Aaron's son)
1998: Rose (Gerald's daughter)
1998: Leanne (Gerald's daughter)
2001: Jason (Gerald's son)
2011: Adele Poe (Adam's daughter)
Most of these are OCs. Can you tell? :/ Andrew, Lucia, Livius, Josh and Arnaud all die in childhood BTW
Jai dies quite young, too.