Thanks to a recommendation by Dominic Albanese, I mail ordered some teas from the Strand Tea Company in Oregon (I put a link to their website below). One of them was their Decaf Apricot flavored black tea, which is quite good. One of the problems with decaf tea is that when you take out the caffeine, you also take out some of the flavor, so that the black tea taste doesn't come through as strongly. I brew it longer (seven minutes as opposed to the usual five) to make up for this, and that helps.
Strand's website says: "Premium Ceylon Black tea decaffeinated by CO2 method, then flavored with apricot juices and marigold flower petals. A bountiful taste of Apricot gives a slight sweetness and wonderful aroma making this our most popular decaf." It's their favorite decaf, but they only offer three, Earl Grey, this, and English Breakfast. I also got some Decaf Earl Grey, also very good, upon which I'll report later.
This is a very smooth tea, full of apricot flavor that is not overpowered by the black tea, even when steeped a long time. There is no harshness to it at all, and it has the mouth feel of a full bodied black tea.
Strand Decaf Apricot: A great apricot-flavored decaf tea, full bodied, but not harsh. This is now in my regular decaf rotation.