I have a rem 22 semi auto take down, but can't find a ser no. any where on the rifle

Hi
here is all the information I could find from the Remington Society of America


Remingtons manufactured after 1921 have a code located on the left side of the barrel near the frame that identifies the year and month of manufacture. The following letters correspond to the months of the year, for example B=January, L= February and so on:
B - L - A - C - K - P - O - W - D - E - R - X

Barrel Code Location Diagram
Click this ^
Don't try to read this ->
It's just a thumb image

Serial Numbers by date (factory record book)
1903 and 1903A3 Production and Serial No table.
1903A4 Snipers.

B - Jan L - Feb A - Mar C - Apr K - May P - Jun O - Jul W - Aug D - Sep E - Oct R - Nov X - Dec

M - 1921 N - 1922 P - 1923 R - 1924 S - 1925 T - 1926 U - 1927 W - 1928 X - 1929 Y - 1930 Z - 1931 A - 1932 B - 1933 C - 1934 D - 1935 E - 1936 F - 1937 G - 1938 H - 1939 J - 1940 K - 1941 L - 1942 MM - 1943 NN - 1944 PP - 1945 RR - 1946 SS - 1947 TT - 1948 UU - 1949 WW - 1950 XX - 1951 YY - 1952 ZZ - 1953 A - 1954 B - 1955 C - 1956 D - 1957 E - 1958 F - 1959 G - 1960 H - 1961 J - 1962 K - 1963 L - 1964 M - 1965 N - 1966 P - 1967 R - 1968 S - 1969 T - 1970 U - 1971 W - 1972 X - 1973 Y - 1974 Z - 1975 I - 1976 O - 1977 Q - 1978 V - 1979 A - 1980 B - 1981 C - 1982 D - 1983 E - 1984 F - 1985 G - 1986 H - 1987 I - 1988 J - 1989 K - 1990 L - 1991 M - 1992 N - 1993 O - 1994 P - 1995 Q - 1996 R - 1997 S - 1998 T - 1999 (*) U - 2000 (*) V - 2001 (*) W - 2002 X - 2003 Y - 2004 Z - 2005 A - 2006 B - 2007 C - 2008 D - 2009 E - 2010 F - 2011 G - 2012

It shows a thumbnail picture of the locations, I'm sorry I tried to enlarge it, but when it placed it on the page, it went back small again.

I guess you'll have to zoom in to look at it.
Just hit control and the + sgn at the same time to enlarge, and control and the - sign to shrink it back.

I hope this helps you identify it better.