I would highly recommend VMP (Video Mount Products) TR series tripod mounts. They are available in both 36-inch/3-feet and 60-inch/5-feet sizes. IMHO they are built very solid and have much better construction compared to the 3-foot Radio Shack tripod (made by Antennacraft) that I had used previously. I used the VMP 36-inch TR-36 model on the peak of my roof with a very large Winegard TV antenna (with a 168-inch boom length and heavy wind load) and have had no problems since it was mounted back in 2009.
In my opinion a discone antenna on a 10-foot mast is not going to be that much of a load on the tripod mount. The 3-foot mount without any guy wires would probably be fine. Of course the 5-foot mount has a larger footprint and therefore can handle a bigger load which may be useful to you especially if you decide to go higher than a 10-foot mast.
Regarding the VMP line of tripods, they came highly recommended to me by a guy who installed TV (and other) antennas professionally. He told me that VMP was the brand that he used because of their solid construction so that was good enough for me.
Solid Signal (located in Michigan) carries both models at the links below. I have purchased from Solid Signal numerous times in the past and have gotten fast delivery, quality customer service and very good and competitive pricing.
VMP TR-36 at Solid Signal
$41.67 ($86.95 list price):
VMP 36-Inch Heavy Duty Tripod (TR-36)
VMP TR-60 at Solid Signal
$65.67 ($112.95 list price):
VMP 60-Inch Heavy Duty Antenna Tripod (TR-60)
