I've been working on this question for my own car and will share a few things.
You didn't say what you're trying to accomplish by using a deep cycle battery.
In my case I wanted to
1) enable longer coasts with engine off and headlights or heater fan on
and EVENTUALLY
2) enable the car to run off a deep cycle battery with the alternator disconnected, for a couple hours or more.
#1 was not so difficult. I ran a pair of cables out the back of the hood and in through the front passenger door, to a 2nd battery on the rear floor. That's a temporary location for "concept testing and proving". It worked. Even a coast of a mile or more only brings system voltage down to about 11.6, which is OK by me.
So, nearly any 12V battery that's compatible with the main one, wired in parallel, will solve that problem. And the pair cranks the starter super strong, regardless of frozen outside temperature here in New England.
#2 is more challenging. I'm concerned about venting of hydrogen gas. Supposedly it only comes from overcharging, HOWEVER I've also heard that cars with battery in trunk typically get a rusted out trunk from frequent or continual venting of sulphuric acid or some component of that noxious stuff.
So I decided to use only EITHER: an AGM (absorbed glass mat) type lead acid battery, OR a lithium LiFePO4 pack. Either type raises the cost out of the $150 category very quickly.
AGM is a type of flooded lead acid battery, aka FLA. Same chemistry as a regular flooded battery but the acid is in a paste and is absorbed into a fiberglass mat. It's practically leak proof and can be installed laying on its side. Disadvantage: for battery life of more than 300-400 cycles, you can only discharge it about 20-25% of capacity. So your 60AH battery becomes a 15-20AH battery if you want to keep it working. You can charge it with your stock alternator, or hook up an A/C charger instead.
LiFePO4 is supposedly super safe and avoids all the fire/explosion concerns of other lithium types. You can discharge it down to 20% of capacity, using 80%, and still get ~2000 charge/discharge cycles. More cycles if you discharge it less. So a 40AH battery would have 40*.8 = 32AH available capacity, not too shabby. That's double the available capacity of a 60AH lead acid unit, and about 1/4 the weight of the lead battery too.
You can't charge it off the alt as the Li based pack is 12.8V and needs higher charging voltage than a 12V battery. I haven't tested that info - maybe if you hook it up to your stock setup it would charge some. But its charging specs are definitely not the same as a lead acid battery. I plan to charge mine nightly from A/C.
Here's a link to one. Note the link on that page to the charger they offer.
Custom LiFePO4 Prismatic Battery: 12.8V 40Ah (512Wh, 30A rate ) with PCM, charge & discharge terminals (48.0) I'm getting an upgraded version that has a 100A limit.