This is my spare tire bike rack. It bolts to the spare tire mount using the spare tire lug studs, and is sandwiched between the mount and the spare. It is based off of a Yakima Sparetime carrier. The rack is tilted to avoid a top tube adapter. The bike is secured using two quick fist clamps.
I based it off of a Yakima Sparetime, but I didn't want to have to use a top tube adapter, nor did I want the bulk of a tire tray. I designed it around my Specialized Stumpjumper Comp, which has a top tube angle of about 15 degrees. I cut the steel with a CNC plasma and a metal bandsaw, but a cutoff wheel would do. I welded a 1/2-13 nut into the bracket, into which a knob with stud (McMaster 60965K362, $12.50) screws. I drilled some holes in the knob, and made a short stainless cable to lock the knob from turning. This prevents someone from walking away with the bike and rack together, as well as any inadvertent unscrewing of the knob on the road. I also welded on some tie down rings at the top and bottom for bungees prior to powdercoating. There is a 1/16" metal plate in the larger center square tube on the rack to make up for the rack OD/bracket ID. I zapped a 1/2" washer onto the end of the 1.25" tube for the knob to pass through. I designed the bracket around my spare, which is 255/75/17, so if your spare is thinner, you may want to make the bracket tube shorter. As it is, it comes out to about flush with the sidewall. The bike is secured using two quick fist clamps. A bungee minimizes wobble, and a cable lock keeps it secure.
After welding and cleanup, the whole business was powdercoated using a Harbor Freight powdercoating setup, and black wrinkle from Powder buy the Pound (https://www.powderbuythepound.com/s-s-black-wrinkle.html).
1x 7x0.125" round plate
1x 3x1x1" square tube (may shorten)
1x 1x1x0.125" plate with 0.53" hole centered
1x 1/2-13 nut
2 to 4x 1x1x0.125" plate (for covering ends of square tube)
2x 15 3/8x1x1" square tubes
2x ~6x1x1" square tubes
2x 6x1" round tubes
1x 2 1/2x1 1/4x1 1/4" square tube
1x 1x2x0.0625" plate
2x standard quickfists (Amazon, ~$11)
1x 1/2-13 knob with stud (McMaster 60965K362, $12.50)
1x 1/2" steel washer