A friend asked me about English-language translations of Las Casas and Oviedo that he could assign as primary-source readings to his students, and I have made him: this overly elaborate list!
In short: you have an embarrassment of options if you're looking for English translations of Las Casas. Oviedo...not so much.
The Spanish colonie, or Briefe chronicle of the acts and gestes of the Spaniardes in the West Indies, called the newe world... (1583)
[EEBO] [Internet Archive]
"A briefe narration of the destruction of the Indies..." in Purchas his pilgrimes (1625)
[ EEBO ]
The tears of the Indians being an historical and true account of the cruel massacres and slaughters of above twenty millions of innocent people... (1656)
[ EEBO ] [ Internet Archive ] [ Google Books ]
Popery truly display'd in its bloody colours, or, A faithful narrative of the horrid and unexampled massacres, butcheries, and all manner of cruelties... (1689)
[ EEBO ]
An account of the first voyages and discoveries made by the Spaniards in America containing the most exact relation hitherto publish'd, of their unparallel'd cruelties on the Indians... (1699)
[ EEBO ]
Modern Translations of Las Casas' Brief Account (A Non-Exhaustive List)
trans. Andrew Hurley, An Account, much abbreviated, of the destruction of the Indies (2003)
[ WorldCat ] [ Google Books ]
trans. Nigel Griffin, A Short Account of the Destruction of the Indies (1992)
[ WorldCat ] [ Google Books ]
Online Versions of Las Casas' Brief Account
Project Gutenberg has the 1689 translation (aka "Popery truly display'd") available in various formats: Project Gutenberg
There used to be an online version of the Griffin translation that has, it appears, now withered away...but as long as we live in the world of the Internet Archive, is anything ever really gone?
Las Casas in English Translation Beyond the Brief Account
Bartolomé de las Casas and the defense of Amerindian rights: a brief history with documents, eds. Lawrence A. Clayton and David M. Lantigua (2015)
[ WorldCat ] [ Google Books ]
David Thomas Orique, To Heaven or Hell: Bartolomé de las Casas's Confesionario (2018)
[ WorldCat ] [ Google Books ]
16th/17th-cen Translations of Oviedo
Note: Oviedo tends to turn up in English translation via fragments, excerpts, and scraps.
The "Summarie" appears in Richard Eden's The decades of the newe worlde (1555)
[ EEBO ] [ Google Books ]
Also, "extracts" from the "Summarie" pop up in Purchas (1625)
[ EEBO ]
Modern Translations of Oviedo
trans. Sterling Stoudemire, Natural History of the West Indies (1959)
[ UNC Press ]
Kathleen Ann Myers, Fernández de Oviedo's Chronicle of America: A New History for a New World (2007) has an appendix with thirty-six pages of Oviedo material translated by Nina M. Scott.
[ UT Press ]
Online Versions of Oviedo
At Vassar, undergraduate students are currently engaged in a multi-year project to translate Oviedo's Historia General de las Indias: The Oviedo Project at Vassar
Last updated: August 26, 2020, by Lauren MacDonald.