It used to be quite possible, even as a solo person, but with the current airline checked luggage restrictions, it's a bit more difficult.
If you go on Southwest, where you can still check two items per person, it's quite doable. If you fly on an airline where you can check 1 item, it's still possible with 2 people.
For two people, with a 1 bag checked luggage limit, you can do the following:
Go to Wal-Mart in the automotive section and get a "Locking Trunk Locker". It is a plastic footlocker that is airline legal as far as size.
Also try to find the largest duffle you can. (Hopefully one that will accomodate two folding chairs.)
Also, you can bring a carryon bag per person, (A 21" rollerbag)
and a personal item per person. (A school bookbag. This is your shower bag)
You should bring the following:
A tent big enough for both of you, plus your gear.
Some type of folding shelter or screen room (EZ-Up type shelters are too big).
Two of the bag folding chairs
Two twin air mattresses or 1 queen
Sheets, blankets, small or inflatable pillows
An air mattress pump
A battery operated or electric lantern
A small light for inside the tent. I like those Coleman Tent Lights that are magnetic
Extra batteries
Two - Three changes of clothes
Laundry supplies in ziplocs if you need to wash
A set of toiletries for each of you
Towel and washcloth for each of you. (I recommend older thinner towel, a big thick one will not dry hanging outside in the humidity, unless you pop it in the dryer each day.)
A clothesline (or you can hang your towel from the poles inside your shelter)
A minimum 40 foot OUTDOOR extension cord
A power strip
Chargers for cell phones, camera, etc.
A small fan
If it's going to be coolish, an electric mattress pad
A lock for the footlocker (not used on the plane, but used on the footlocker while you are away from the tent)
Rain Gear
I find those quick clips in various sizes are good for lots of things like hanging the lantern from your shelter, hanging keys on a loop inside the tent, etc.
Garbage bags
Large ziplocs
a package 8 inch cable ties and a small set of wire cutters to clip them if you use them.
If you have room, a small string of christmas lights and a timer, that way when you return to the campsite at night, it is easier to find your site.
In your footlocker and large duffle, put the tent, shelter, chairs, linens, your liquid toiletries, air mattress, your clothing. On the tent, shelter and chairs, don't pack the original bags they came in. Just extra weight and harder to pack the tent and stuff back into them.
In your carryon and personal item, pack anything that is small but heavy, such as your lantern, extension cord, tent stakes, power strip, air mattress pump., extra shoes
You don't need to worry about your clothes, tent, bedding, chairs being bothered, but if there is anything you want to leave at camp, then lock it inside the footlocker while you are out.
Hope this helps!!!