The Remington model 510 Target Master was made from 1939-1962.
http://remingtonsociety.com/rsa/service
Your Remington model 510 Target Master will bring between 195-250 dollars in the condition that you describe.
Find the serial number and google the Remington sight. They should have records of when the weapon was produced.
i have a22 cal bolt 510 target master to contact me tolley6913@hotmail.com
current value of a 1941 Remington 510 22cal rifle
http://www.remingtonsociety.com (forums)
They were produced from 1939-1962, and I've seen them at auctions going for $90-300.
You can find Remington Date of Manufacture codes at www.rimfirecentral.com in Remington Forum
Numrich gun parts
According to all of the Remington date code decoders I have found, your rifle was manufactured in Feb 1946. See http://rimfirecentral.com/forums/showthread.php?t=9555 for reference to the chart. Hope this helps!
I would try checking with some of the places that list parts for it on the Remington Society of America's Service and Parts link here: http://remingtonsociety.com/rsa/service With a 510 I'm not sure if they will care or not but some places are a bit hesitant to sell a bold due to concerns about proper fitting (head space) by a gunsmith???