You can either use split + lapply from base R:
library(stargazer)
lapply(split(df, df$year), stargazer, type = "text")
or by:
by(df, df$year, stargazer, type = 'text')
Result:
===============================================================
Statistic     N      Mean        St. Dev.      Min      Max    
---------------------------------------------------------------
Population    10 9,083,988.000 7,541,970.000 491,723 21,759,420
Distance..km. 10   5,637.500     2,385.941    2,211    9,500   
year          10   2,008.000       0.000      2,008    2,008   
---------------------------------------------------------------
===============================================================
Statistic     N      Mean        St. Dev.      Min      Max    
---------------------------------------------------------------
Population    10 9,361,404.000 7,798,880.000 496,963 22,549,547
Distance..km. 10   5,637.500     2,385.941    2,211    9,500   
year          10   2,009.000       0.000      2,009    2,009   
---------------------------------------------------------------
===============================================================
Statistic     N      Mean        St. Dev.      Min      Max    
---------------------------------------------------------------
Population    10 9,645,370.000 8,065,676.000 502,384 23,369,131
Distance..km. 10   5,637.500     2,385.941    2,211    9,500   
year          10   2,010.000       0.000      2,010    2,010   
---------------------------------------------------------------
df$year: 2008
[1] ""                                                               
[2] "==============================================================="
[3] "Statistic     N      Mean        St. Dev.      Min      Max    "
[4] "---------------------------------------------------------------"
[5] "Population    10 9,083,988.000 7,541,970.000 491,723 21,759,420"
[6] "Distance..km. 10   5,637.500     2,385.941    2,211    9,500   "
[7] "year          10   2,008.000       0.000      2,008    2,008   "
[8] "---------------------------------------------------------------"
-------------------------------------------------------------------------- 
df$year: 2009
[1] ""                                                               
[2] "==============================================================="
[3] "Statistic     N      Mean        St. Dev.      Min      Max    "
[4] "---------------------------------------------------------------"
[5] "Population    10 9,361,404.000 7,798,880.000 496,963 22,549,547"
[6] "Distance..km. 10   5,637.500     2,385.941    2,211    9,500   "
[7] "year          10   2,009.000       0.000      2,009    2,009   "
[8] "---------------------------------------------------------------"
-------------------------------------------------------------------------- 
df$year: 2010
[1] ""                                                               
[2] "==============================================================="
[3] "Statistic     N      Mean        St. Dev.      Min      Max    "
[4] "---------------------------------------------------------------"
[5] "Population    10 9,645,370.000 8,065,676.000 502,384 23,369,131"
[6] "Distance..km. 10   5,637.500     2,385.941    2,211    9,500   "
[7] "year          10   2,010.000       0.000      2,010    2,010   "
[8] "---------------------------------------------------------------"
The disadvantage of these two methods is that they print out the tables twice (once from stargazer output, another from lapply/by). To get around this, you can use walk form purrr to only call stargazer for it's side-effects:
library(dplyr)
library(purrr)
df %>%
  split(.$year) %>%
  walk(~ stargazer(., type = "text"))
Result:
===============================================================
Statistic     N      Mean        St. Dev.      Min      Max    
---------------------------------------------------------------
Population    10 9,083,988.000 7,541,970.000 491,723 21,759,420
Distance..km. 10   5,637.500     2,385.941    2,211    9,500   
year          10   2,008.000       0.000      2,008    2,008   
---------------------------------------------------------------
===============================================================
Statistic     N      Mean        St. Dev.      Min      Max    
---------------------------------------------------------------
Population    10 9,361,404.000 7,798,880.000 496,963 22,549,547
Distance..km. 10   5,637.500     2,385.941    2,211    9,500   
year          10   2,009.000       0.000      2,009    2,009   
---------------------------------------------------------------
===============================================================
Statistic     N      Mean        St. Dev.      Min      Max    
---------------------------------------------------------------
Population    10 9,645,370.000 8,065,676.000 502,384 23,369,131
Distance..km. 10   5,637.500     2,385.941    2,211    9,500   
year          10   2,010.000       0.000      2,010    2,010   
---------------------------------------------------------------
Note:
All methods above works for latex output (type = "latex"). I only set type = "text" for demonstrative purposes.