How many times do you intend to cycle this thing? If you're just going to use it a few times per year, then who cares if your battery can only handle 10 or so full discharges... espically if it has a 2-year free replacement warranty
. In that case, I'd just suggest getting a cheap lawn tractor battery, or probably even better - a 17Ah UPC battery. I think you can find thoes as cheap as $20-30. Harbor freight sells a car jumper unit for between $30-40, and it has a 17Ah SLA in it... you could buy that and yank the battery out of it...
However, if you're thinking you're going to cycle it every night, you should probably do it right.
One thing that comes to mind is a powerwheels battery. They are deep cycle, and relitively cheap. Since you're wanting to run 9amps (2x4.5 amp bulbs) for .75 hours, then the battery would be 100% depleated if you had a 6.75ah battery. in theory, a 13.5ah battery would be at 50% after 45 minutes of runtime.
If I were your, I'd just get a cheap lawn tractor battery from walmart, since I've only actually been out at night once with my buggy, and I probably only ran my headlights for half an hour. However, we are both different - you might like to ride every night...
I came across this today also BTW, which seems to be a pretty good read. This agrees with what I said about deep cycle vs lawn tractor batteries. You may learn something here too.
http://powerwheelscd.com/images/gard...batteries1.pdf
I haven't looked at prices of the powerwheels batteries, so I don't know if they fit your budget or not, thats just something that came to mind.