I'd argue that there has been enormous political instability in Guyana's recent history, with a lot (not all) of it traceable to the ethnic split that occurred between the Jagan (Indo-Guyanese) and Burnham (Afro-Guyanese) factions of the PPP in the late 1950s. In 1954, the British deposed the elected government and sent troops into Guyana because they felt that Jagan was a radical communist. Cheddi and Janet Jagan both spent time in jail on ridiculous charges and the British government encouraged the Jagan-Burnham split and then repeatedly changed the electoral system to try to give Burnham the advantage.

There were huge riots and strikes in Georgetown in the early 1960s, with the worst resulting in a number of deaths. Burnham took power in a minority government in 1964 and then proceeded rig elections and stoke the racial divide to keep himself in office until his death. Opponents of his rule often wound up dead, most famously the Pan-Africanist scholar Walter Rodney, who was killed by a bomb apparently planted by a sergeant of the Guyanese Defense Force (who subsequently left the country on a government plane and was later found living under an assumed name in French Guiana). By the time Burnham died in 1985, the economy was in freefall.

Things have stabilized a good deal since then, but the country still has a lot of problems. A grenade was thrown at a newspaper office just a couple months ago. In 2006, the gang leader Rondell Rawlins accused the government of kidnapping his girlfriend and carried out reprisal massacres in Bartica and Lusignan, killing 24 people. He also probably assassinated Agriculture Minister Satyadeow Sawh, although the main opposition party accused the government of using Rawlins as a scapegoat to cover up the actual motive for the murder. Someone claiming to be Rawlins called a newspaper and confessed to the Lusignan attack, but denied killing the minister.

I admit I don't know a great deal about Fiji's history, so I'm not able to compare the two, just wanted to point out that Guyana has not been exceptionally stable compared to the rest of the British West Indies (with the exception of Grenada, of course).