It's only 109 MB in size zipped up for both coh's and cov's music.
Since they were publicly available at one time, they're probably on some website for download. With the song list, you got something to hunt for.
M9_loop was the main theme song for cov when you first logged in.
Song list/sound effects for COH.
ArgosyIndustries_loop.mp3 Texture19.mp3
ArgosyIndustries.mp3 Texture1-Boneyard.mp3
AtlasPark1.mp3 Texture20.mp3
BastionofRegret.mp3 Texture21.mp3
BloodyLane.mp3 Texture22.mp3
BoomTownSector.mp3 Texture2-Boomtown.mp3
COHTheme_loop.mp3 Texture3.mp3
FoolsGold_loop.mp3 Texture4-ChironMed.mp3
Funk.mp3 Texture5-CoromanManufacturing.mp3
Heroes1_loop.mp3 Texture6-CreyCove.mp3
Heroes2_loop.mp3 Texture7-DarkAstoria.mp3
Heroes3_loop.mp3 Texture8-Eden.mp3
Heroes4_loop.mp3 Texture9-EveretteLake.mp3
Heroes5_loop.mp3 TheCannonade.mp3
Ominous.mp3 Theme1.mp3
Orchestral1_loop.mp3 Theme2_loop.mp3
Orchestral2.mp3 Theme2.mp3
Orchestral3_loop.mp3 Theme3_loop.mp3
Orchestral4_loop.mp3 Theme3.mp3
Percussion_loop.mp3 Theme4_loop.mp3
Texture10_Evil.mp3 Theme4.mp3
Texture11_SerpentsTeeth.mp3 Theme5_loop.mp3
Texture12_RedRiver.mp3 Theme5.mp3
Texture13_Hive.mp3 Theme6_loop.mp3
Texture14_WaveLanding.mp3 Theme6.mp3
Texture15.mp3 Theme7.mp3
Texture16.mp3 Theme8.mp3
Texture17_Serpentine.mp3 Theme9_loop.mp3
Texture18.mp3 Theme9.mp3
COV's list
J11_loop.mp3 J33_loop.mp3 M10_loop.mp3 M17_loop.mp3 M5_loop.mp3
J13_loop.mp3 J35_loop.mp3 M11_loop.mp3 M1_loop.mp3 M6_loop.mp3
J17_loop.mp3 J39_loop.mp3 M12_loop.mp3 M28_loop.mp3 M7_loop2.mp3
J22_loop.mp3 J45_loop.mp3 M13_loop.mp3 M2_loop.mp3 M8_loop.mp3
J25_loop.mp3 J5_loop.mp3 M14_loop.mp3 M32_loop.mp3 M9_loop.mp3
J29_loop.mp3 J6_loop.mp3 M15_loop.mp3 M3_loop.mp3
J30_loop.mp3 J7_loop.mp3 M16_loop.mp3 M4_loop.mp3