From the 2003 Composer compilation promo featuring film and television scores cd. This selection conducted / adapted by Eric Schmidt and recorded at Paramount Pictures Scoring Stage M, Hollywood.
My sincere thanks to Gareth Bramley for taking the time to list out the title segments for the suite, they are as follows:-

Track titles - timings are approximate:
0:00 - 0:44 - Opening medley.
0:44 - 1:43 - 'The Cartwright Brothers' - this is the incidental theme Sukman wrote for season 11 of 'Bonanza' in 1969. He scored 31 episodes - 27 from this season; 2 each from seasons 13 and 14 (both 1972).
1:43 - 3:50 - 'Manolito', used throughout the series.
3:30 - 5:00 - 'Moonfire' the theme written for the character of the same name (played by Barbara Hershey) in the episode 'The Peacemaker' (S1:E25) (3/3/68).
5:00 - 7:32 - 'Montoya' - Don Sebastian Montoya's theme, used throughout the series.
7:32 - 9:00 - 'Riding The Trail' (Buck's Theme), used throughout the series. Lyrics were later added by Joe Lubin for the track on the 2 record set recorded by Xanadu Pleasure Dome (released 1970).
9:00 - 9:50 - This short piece may be an introduction to the following section. I seem to recall it played out when Blue visited his late mother's grave.
9:00 - 11:02 - 'Blue's Theme' used throughout seasons 1-3.
11:02 - 12:19 - 'Cantina' - used to accompany the cantina scenes in the series.
12:19 - 13:06 - This theme was used in the episode 'The Little Thieves' (S3:EP13) (26/12/69).
13:06 - 14:59 - This theme seems familiar - but it's not 'Friends & Partners' as per the episode, so could be 'El Burrito' (The Donkey) which I do not know.
14:59 - End - Medley.