Create the login on primary db first. And then, give it the permissions you want. After that, get the SID of the login by using this code:

select sid from sys.syslogins

where name = 'login_name'

And finally, create the login on read-only db with the same SID of the login.

sp_addlogin 'login_name', @passwd='mellon',

@sid = the_sid, @defdb='MASTER'