If you wish to reprint any song that is not in the public domain in a songbook, songsheet, or any other print publication (e.g. magazine), you must obtain permission from the individual or company that owns the song.
The copyright notice in Rise Up Singing or Rise Again can usually give you some clues to how to track down who owns and administers the song.
Cost. Although the rate that can be charged for use of copyrighted material in recordings is set by law, there is no such guideline for print licenses. Basically anyone owning a song can charge whatever they wish or simply refuse to allow a song to be reprinted at all. (When we were licensing songs for Rise Up Singing, one music publisher demanded that we pay $5000 to license their one song - which we of course could not do!)
Online Searches: There are a number of online databases you can use to search for who controls print rights.Third party administration of print rights. Individual composers and smaller music publishers often assign print permission administration rights to another larger company. Hal Leonard Music in particular controls administration rights to a huge number of song catalogs at this point. As a result, the copyright owner listed in an online search may not be the place you need to go to get print permissions. They should, however, be able to tell you who administers print rights for them if this is the case.