beamdeckjoists
I am re-posting this because my original post had poor drawing and caused a lot of confusion.
See image below. I have a joist that is cantilevered 4' 10" (colored in cyan for quick reference), which I wish to support by a double 2×12 (or smaller?) beam which colored in purple for quick reference.
My question is: Is this acceptable? The span of the "purple" beam would be ~14', but all it's really needed for is to support those joist that are cantilevered. 
OK first let me say that if you're going to be making major structural changes to a building (and this counts as a pretty serious structural change in my mind) it would be well worth your while to get an engineer or other qualified building professional to help you with your design. If you just "wing it" you may be endangering the house and its occupants. There may also be legal or insurance-related ramifications to doing this outside the proper channels. However, let me offer these pieces of advice:
As Tester101 mentioned, in this application there is close to no load on the rim joist, since your actual joists are supported by the beam. Nailing through the rim joist into the end of the other joists will be fine. I've built plenty of decks like this.
Here's a study that was done on end nailing, and the relevant recommendations:
Recommendations
Nails driven into the end grain of wood do resist both static and impact loads. However, additional research is required in several areas. Of the 4,723 data points on the relationship of specific gravity to nail withdrawal strength, only 294 data points were from tests of nails with a diameter larger than 2.52 mm (0.099 in.). Therefore, research is needed on endgrain withdrawal capacity of nails with a diameter greater than 4.1 mm (0.163 mm) so that Equation (5) can be further developed.
Furthermore, none of the studies evaluated repetitive loading of nails from the end grain since joints in service typically do not experience strictly static or impact loading. Repetitive loading may cause end-grain withdrawal capacity to significantly decrease over time.
There is conflicting data on how threaded nails perform in comparison with smooth shank nails when withdrawn from the end grain. Three studies showed an increase in nail withdrawal capacity whereas one study showed a decrease. Since the use of threaded fasteners in construction is increasing, more research is needed to determine the effects of surface characteristics on end-grain withdrawal.
Finally, more research is needed to determine the long-term withdrawal strength of nails driven into end and side grain. The data in this report suggest that over time end-grain and side-grain withdrawal capacity may become equivalent. Very few test replicates measuring the effect of time delay on withdrawal strength were conducted, and more tests need to be run to clarify these limited observations.
If you still feel like you need more support, yes, you can find something like this: 
at most hardware stores. If you're working with pressure treated lumber remember you will need galvanized plates and connectors.
Best Answer
While your approach is fine, but I prefer to add an edge beam as shown red in the sketch below. Then you only need to run the diagonal in between the beams.