Two months is a non-issue. The battery maintainer is more important here.
Full or empty?
Race Director
Joined: Apr 2017
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From: Virginia
You're most likely going to see a lot of back and forth here between full and 1/2 full, however for just storing your C7 for 60 days it doesn't really make any difference one way or the other.
Other's will probably comment that you need to put fuel stabilizer in the tank as well, that's hogwash too.
Other's will probably comment that you need to put fuel stabilizer in the tank as well, that's hogwash too.
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You can find a number of threads on this subject. You will find there are two schools of thought. Two months is not that long so either way if fine.
Here are the two school of thoughts.
1. When storing your car you should fill the tank. That is so that air/condensation is not in the tank and rust, corrosion will not occur.
2. You should only fill your tank 1/4 full. This prevents the sensors in the tank from becoming gummed up. If you search this thread section will find some knowledgeable thoughts and information on this subject.
But, two months, park it, hook it up to a battery maintainer and no worries.
Here are the two school of thoughts.
1. When storing your car you should fill the tank. That is so that air/condensation is not in the tank and rust, corrosion will not occur.
2. You should only fill your tank 1/4 full. This prevents the sensors in the tank from becoming gummed up. If you search this thread section will find some knowledgeable thoughts and information on this subject.
But, two months, park it, hook it up to a battery maintainer and no worries.
Pro
Joined: Jan 2014
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From: Huntersville, North Carolina
I don’t know your circumstances but, I had planned to park mine for 4 months and it ended up being 3.5 years. I’d put full stabilizer in the tank if there is any chance it will be longer then 2 months.
Instructor
Joined: Oct 2011
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From: Geneva NY / The Villages, FL
As stated above, there are two schools of thought on this one regarding C7 storage. Most often pertaining to winter time storage and potential damage to the sensors in the fuel tank. To confuse matters, let me offer another this: I like to fill my vehicles when they get to be around a half tank. I believe the fuel helps cool the fuel pump and hopefully extend its life. For this reason, my corvette sits with 3/4 to a full tank almost all summer. Perhaps the sloshing gas helps keep the sensors clean in our corvettes? If not, what would be the difference summer to winter?
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Team Owner
Joined: Apr 2013
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From: Chirper Island
As said, recently TPTB say to store it closer to the empty point rather than full to avoid the fuel sensor sulphurizing. According to "them" when it's sitting and covered in fuel, it allows for sulphur build-up because it is not getting sloshed around like it is when in use.
That said, I think it is a crap shoot, because both my '05 and my '14 never sat for more than two weeks in the collective 400,000 miles on them and yet both cars had fuel sensors go bad.
If you never drive your car, then your guess is as good as mine.
And FWIW, a bad sensor is not that big a deal. That's what the trip ODO is for.
That said, I think it is a crap shoot, because both my '05 and my '14 never sat for more than two weeks in the collective 400,000 miles on them and yet both cars had fuel sensors go bad.
If you never drive your car, then your guess is as good as mine.
And FWIW, a bad sensor is not that big a deal. That's what the trip ODO is for.
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My $0.02. I filled my '08 (similar system) every winter. After a few years of doing that my fuel gauge went wacky and the level sensor needed to be replaced. Not an easy or inexpensive job. After that 1/2 full for me and never had the fuel gauge problem again.
Melting Slicks
Joined: Aug 2009
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From: Schaller Iowa
In every vehicle I have, cars and pickups I put in a bottle of Techron every third tank fill up. Never have had issue to date. I've always topped off the tank before winter storage with both Sta-bil and Techron and again no issues.
Team Owner
Joined: Apr 2013
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From: Chirper Island
I should add as aside: I added Techron regularly to those two Vettes. I also added Techron to the other three (140,000 miles cumulative) with no issues on those ones. 
p.s. Techron label directions say only every oil change. Make what you will of it.
p.s. Techron label directions say only every oil change. Make what you will of it.
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Do as you like as either way will be fine. Just hook it up to a battery tender/maintainer to avoid a possible dead battery.
Race Director
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From: Bonneville Salt Flats
The same as John Deere recommends for mowers and such stored over the winter, full tank with the correct amount of appropriate fuel stabilizer... (see any of their Manuals online). Add the stabilizer a little at a time while filling the car and drive for a short while to get the treated gas everywhere. I've been doing so in all my non-regularly driven collector vehicles for years without issue. All the best. 
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I would put a battery tender on it & stabilize the fuel for peace of mind & be done with it
