Well that would be the cases I described, where scientists have calibrated C-14 curves with objects of known ages and with things like lake varves, tree rings, and stalagmites. Now, I'm not sure what sort of support you're looking for on things like this, but here are a few citations (some to web sties, others to more scientific resources)....
Calibration of radiocarbon dates - Wikipedia
Radiocarbon Calibration
C-14 Information and Labs
First, as Polymath pointed out, C-14 dating is only applicable to objects that are less than ~50,000 years old. So any objects older than that would have to be dated using other methods.
And if you read through the resources linked above, you'll see how some of the calibrations extend back over tens of thousands of years, indicating that the decay has not changed over that time.
The method
The historical perspective on the development of radiocarbon dating is well outlined in Taylor's (1987) book "Radiocarbon Dating: An archaeological perspective". Libby and his team intially tested the radiocarbon method on samples from prehistoric Egypt. They chose samples whose age could be independently determined. A sample of acacia wood from the tomb of the pharoah Zoser (or Djoser; 3rd Dynasty, ca. 2700-2600 BC) was obtained and dated. Libby reasoned that since the half-life of C14 was 5568 years, they should obtain a C14 concentration of about 50% that which was found in living wood (see Libby, 1949 for further details). The results they obtained indicated this was the case. Other analyses were conducted on samples of known age wood (dendrochronologically aged). Again, the fit was within the value predicted at �10%. The tests suggested that the half-life they had measured was accurate, and, quite reasonably, suggested further that atmospheric radiocarbon concentration had remained constant throughout the recent past. In 1949, Arnold and Libby (1949) published their paper "Age determinations by radiocarbon content: Checks with samples of known age" in the journal Science. In this paper they presented the first results of the C14 method, including the "Curve of Knowns" in which radiocarbon dates were compared with the known age historical dates (see figure 1). All of the points fitted within statistical range.
The page goes on to describe how the collection and analyses of additional data indicated that the decay rate is constant and the method is reliable.