Is there a human readable easier version to represent PGP Private keys?
Apparently this answer will be updated as OP develop an understanding of his application. I've never used PGP, but general public-key cryptography concepts are always applicable. 


  entering a private key on a website whenever you need to do something is troublesome


You can let clients derive their keys through memorable string - the user agent first derive a seed using a secure key derivation function (KDF) from 1) the user-supplied string, and 2) a random salt, then the seed is fed to a cryptographic deterministic random bits generator (DRBG), then the key-pair generation is run using the just-seeded DRBG. 

Normally a hard-to guess 16-character string with upper and lower case letters and digits is a minimum. The salt should be a string of at least 16 fully-random bytes. 


  But we also cannot maintain a central database for username/password


If you don't have a database of users, how do you authenticate them (recognize actual users from outsiders)? There is a solution: Use primitives that binds the authenticator to the public key, such as ECQV implicit certificate scheme, or identity-based encryption (IBE). These are not commonly-used public-key cryptography functionalities, and their post-quantum equivalents are far from mature.