This is clearly a polygamous situation as there just aren't enough males so that each female gets a unique male.
We start off with making four initial bonds:
Boy 1 => Girl 2 (after 1 year when she is 19 years of age)
Boy 1 => Woman 1
Boy 2 => Girl 1 (after 2 years when she is 19 years of age)
Boy 2 => Girl 3 (after 3 years when she is 19 years of age)
Each bond is aimed at making 6 babies so as to allow some genetic variation later on.
Assuming that boy-girl ration in offsprings is 1:1, there would be 12 new boys and 12 new girls in 7 years.
After about 12 years girl 4 would reach 19 years and would be ready to participate in the process (if she chooses). Boy 2 would be 28 years old then so it would be a slightly odd pair, but within current social norms anyway.
After 19 years the population of the island would be nearly 8 (initial) + 24 (first generation) + 6 (first generation, delayed) = 38 individuals, 29 of which (2 initial boys + 3 initial girls + 24 of first generation) are still in procreation age.
(12 x 12) + (2 x 3) = 150 different mating combinations are now possible (considering no incest). My idea would be to reproduce slowly, taking into factors such as problematic genes (such as disease vulnerability and IQ). In this way you can allow all members to procreate while also applying some eugenics.
EDIT TO ADD
Here is a chart for the long term process. Males are presented as letters (a and b for Boy1 and Boy2 respectively) while females are represented as numbers (1, 2, 3, 4, 5, 6 respectively girls 1-4 and women1-2)
There can be types of repopulating plans. First one centers on self respect and dignity (no incest or cross pairing) while the other centers on genetic diversity and an option for later implementation of eugenics. The first chart is shown below. The x-axis represents time (in years) as alphabets (year 0 is now while year A means after 1 year, B means after 2 years and so on).
Correction: Girl 4 is missing from the chart. she joins in at year L (12 from the start) when she is 19 years old and is paired with b.
I will try and make the second chart sometime.
Here is the second chart. The second generation children pairing can go the same as in chart 1. The main difference between chart1 and chart2 is how people of generation 1 are paired. Chart 2 includes girls at ages 18 (instead of 19 as in chart 1) and includes cross pairing for increased genetic diversity.