Certainly, you can do this, but do you need it? If the car starts easily with the existing battery, you probably don't need anything bigger. If it doesn't, are you sure it's the battery that's at fault?
If you've added a lot of high-current equipment, and I can't imagine what, in a Sprite, that might be, then the first priority should be a larger alternator, then a battery. A larger battery will help only if that extra stuff is turned on for a short time relative to the off-time--so there is time for the battery to recharge.
If you do install the battery in the trunk, you obviously must protect the car from battery leakage and make sure it is well supported and can't come loose on a bump. You also need to think out where you will locate the high-current lead, so it is not damaged by road debris, chafing, passengers, and so on. This is what concerns me the most--greater chance for a short circuit to the chassis and potentially a fire.
So, unless you have a genuine need, I would pass on this idea. By a "genuine need" I mean something like difficult cranking on cold mornings, which I'm told you occasionally have in Ottawa, and, then, you're sure it's the battery at fault. Even in that case, a better-quality, original-size battery might be all you need. You can get some pretty good batteries these days.