Please let me know if this is possible.

A Parker 61 with cartridge/converter filler is very similar to what you are looking for.

The short answer is that anything can be done, given sufficient money and time. The sensible answer is no. If you want a C/C "51" you may be able to find one ready made. Parker made such a pen very briefly around 1960. It was pretty much an unmitigated disaster, and Parker very quickly withdrew it.

One of the most remarkable features of the "51"s is their original filling mechanisms that have passed the test of time. Take that away, you can't really call it a Parker "51" anymore...

Nevertheless, if it's the appearance of a Parker "51" you're after with a C/C filler, I believe there was a Parker 51 SE released in 2002 which you may be able to find with relative ease Just keep in mind that they don't come cheap, and the materials used are quite cheap compared to original "51"s

Or you can buy a Parker 100... Not exactly the same as a 51, but gorgeous nonetheless.

Or you can buy a CC Parker 61 which is similiar, though a little thinner than a 51. Since most pen heads use converters rather than cartidges anyway, I'm not sure what advantage there would be in converting a 51- you're still filling from a bottle.