The Painswick baptism of 1812 is certainly a good candidate for Charles. The parents Samuel and Elizabeth (Birt) married in 1803.
Gloucestershire : Painswick : St Mary : Phillimore's Transcript : "Parish Register" database, FreeREG (
https://www.freereg.org.uk/search_records/5817df8fe93790eb7fb8601b : viewed 29 Jul 2021) marriage Samuel King to Elizabeth Birt 29 Mar 1803
One tiny argument against is that Charles would only have been 29 for the June 1841 census and adult ages were rounded down to the nearest five years. However, many people were not super-precise about ages and you can only assume he was born around 1807-1812 not precisely in 1811.
I can't find a suitable death record for Charles which is very strange for this period. The death year of 1846 is just an estimate. There's no documentary support.