Is there no wall on the front?
Going with these dimensions, 24"/61cm x 11.5"/29cm x 14.25/36cm = 47liters available using 3/4"/18mm lumber.
47liters is about 1.7cuft. And a single 15" take about .15cuft of room. SO with a pair of 15's you are down .30cuft. So now we are looking at 1.4cuft or about 38liters roughly. So this is using all the volume available. Which is impossible. So it would be very hard to mount these woofers in the space you are given. A single 15 would be easy enough. But looking straight at the bike's front wont allow you to mount the woofer vertically unless towards the middle. 36cm is not enough room to mount to. You could mount a woofer in a PPSL sealed configuration.
Just think sealed and a lot smaller. Wont go as low but you could make the cabinet as big as you have available.
This is a sealed version. You would have to orientate the dimensions to fit your space. Just look at the bottom half. That is a pair of 10's. You could also design a 6th order bandpass cabinet. Which would have the woofer in a sealed enclosure firing into another enclosure that is ported. You would only see the port hole.
So many designs out there but with a pair of 15's trying to be crammed in a little amount of space it is hard to design anything that will go very deep. I would suggest using smaller woofers or using a single 15. Or if you must PPSL sealed might work for you. Porting will be tuned high because of limited space. So you could port around 50hz which would be great for kick drum and what not but would be limited to this and above. SO not much dubstep or other bass heavy music is going to pound from this bottom end.
If this is going to be used outside then a small single 10" horn bottom end would be perfect for you. Low wattage needed and high spl. These 15's would be good ported around 42hz in a proper size enclosure. You dont have that available. Why not build a full range cabinet that plays everything instead of a mid/high and sub configuration?
If I was limited I would build one of Bill Fitzmaurice's Jack 12's or 15's. Everything you need and only need small amounts of watts.