OK, lets list the courses that Christoph and I have been able to identify. This is pretty much been done by online research, so some of these attributions may be not necessarily 100% watertight. We would of course welcome any additions or alterations to this information! We will do it on a country by country basis and the courses are in no particular order.
ARGENTINA
SIERRA DE LOS PADRES GOLF CLUB, Sierra de los Padres, Mar del Plata, Buenos Aires Province - 18 holes
The course was built in 1955, originally designed by the engineer Luther Koontz, and constructed by Alfranco S.A., a company in charge of the urbanization of Sierra de los Padres.
OLIVOS GOLF CLUB, Buenos Aires - 36 holes originally, now 27 holes
The course was designed by Luther Koontz and opened in 1952
MARAYUI COUNTRY CLUB, Chapadmalal, Buenos Aires Province - 9 holes
Course originally designed by Luther Koontz, later rebuilt by Ron Fream. Year not known.
SANTA TERESITA GOLF CLUB, Santa Teresita, Buenos Aires Province - 9 holes
Designed by Luther Koontz, course opened in 1958.
GOLF CLUB SIERRA DE LA VENTANA, Sierra de la Ventana, Buenos Aires Province - 9 holes added
Koontz added a new nine to the existing nine hole course in 1951
GOLF CLUB ARGENTINO, Del Viso, Buenos Aires Province - 18 holes
Designed by Koontz in the 1950s when the club moved from their earlier location in Palermo. Koontz had an involvement in their earlier course, designing a drainage system. Perhaps he made design changes as well, although this is not confirmed.
CLUB NAUTICO SAN ISIDRO, San Isidro, Bueno Aires - 18 holes
Originally planned by Mackenzie in 1930, but the club had difficulties and only 9 holes had been built by 1936. In 1948 Koontz was put in charge of making an 18 hole course and this was finally opened in 1955.
CLUB AMANCAY, High Sierra, San Juan, original 9 holes, now 18 holes
Koontz designed a 9 hole course for this club which was established in 1958.
GOLF CLUB VILLA GESSELL, Villa Gesell, Buenos Aires, original 9 holes, now 18 holes
The course was designed by Koontz and opened in 1967.
LINKS PINAMAR, Pinamar, Buenos Aires - originally 9 holes, now 27 holes
Koontz designed 9 hole course in 1944, the "Cancha Chica". Additional 18 holes built in 1983
NECOCHEA GOLF CLUB, Quequen, Necochea - original 9 holes, now 18 holes
Koontz designed a 9 hole course on moving terrain near the ocean with maritime pines. The later nine holes (not by Koontz) is flatter and further inland.
MARINE IGNACIO GOLF CLUB, Rio Cuarto, Cordoba - 18 holes
Designed by Koontz in 1955, the club was formed later in 1959.
CHAPELCO GOLF, Pilar, Buenos Aires Province - 6 holes originally
A 6 hole course was laid out by Koontz in the 1930's for Henry Martin, an Englishman who had purchased a site of 33 acres in Pilar. Landscaping of the site included a cricket ground and a 6 hole golf course laid out by Koontz. In late 1980s Nicklaus designed a new course on the expanded site.
JOCKEY CLUB DE ROSARIO, Rosario, Santa Fe - 18 holes
Designed by Koontz, first nine opened in 1958 and the second nine in 1960.
SAN ANDRES GOLF CLUB, San Andres, Buenos Aires province
Koontz redesigned some greens on the course laid out by Mungo Park, according to David Edel, years not known.
SAN NICOLAS GOLF CLUB, San Nicolas, Buenos Aires - 9 holes originally
Koontz designed an original course of 9 holes starting in 1958. The course has been changed since.
LLAO LLAO GOLF CLUB, Bariloche - 9 holes originally
According to internet sources the course was designed by Alberto del Solar Dorrego and constructed by Luther Koontz, date not known.
LOS LAGARTOS COUNTRY CLUB, Buenos Aires - original 18 holes
Possibly designed by Koontz in 1969 (one year before his death), and later extended to 27 holes by the Serras in 1988.
CHACO GOLF CLUB, Chaco
Nine holes built in 1944 and shortly after 12 were in play, designed by Koontz with Arthur Short.
CHILE
LA DEHESA GOLF CLUB, Lo Barnechea, Santiago, Chile
A design by Koontz in the mid to late 1950s, according to David Edel (from El Golfer Argentino magazine).
CLUB DE SPORT FRANCES, Santiago
In 1955 a flat 18 hole course was laid out and shortly after Koontz was called in and he designed a 12 hole course, along with a pump system to irrigate the course with river water.
BRAZIL
SAN FERNANDO GOLF CLUB, San Fernando Vila, Cotia - 18 holes
New course by Koontz, opened in April 1958.
URUGUAY
CAMPO DE GOLF DEL CANTEGRIL, Punta del Este - 18 holes, 9 holes added
Course was originally a 9 hole layout by Alex Philp for the Punta del Este Golf Club. On this site and with additional local government land, Koontz extended it to an 18 hole course in 1947. Whether he simply added a new 9 or whether he modified any of the original holes is not known.
That is 23 courses by my reckoning, not far short of the 27 or so that David Edel thinks Koontz designed. Hopefully we can find a few more.