So you want to get the kids out of the house, but also don't want to let them out of your sight. Build a sandpit? No, because you don't want to dig up your lawn either. Why not build a sandbox instead? It's simple and easy, although the grass underneath will die unless you make the considerable effort to move box and contents every few days.
You can make a simple but serviceable wooden sandbox from a sheet of 1/2" thick plywood for the box and a cheaper 1/4" sheet for a base. Cut one 4' x 8' sheet into three 16" x 8' strips. Bisect one strip into a pair of 4' lengths. Form the four panels into a 4' x 8' x 16"-high rectangular open-topped box (make it shorter if you wish by trimming the long panels equally).
Fasten 2" long wood-lath stakes at ends and every two feet along the outsides of plywood panels, and hammer stake ends into the soil to hold the panels down. Fasten the galvanized-steel right-angle truss plates you bought from the hardware store inside each corner—running self-tapping drywall screws through holes in plates, through ply panels, and into end stakes.
Make triangular corner seats with scrap wood cleats fastened underneath to fit the edges of the plywood sides. Glue and nail the seats to the ply and corner stakes, and sand the seat—the edge facing into the box especially. Finish seat and box with paint or outdoor varnish to bind in any potential splinters.
As an additional antisplinter measure, around the upper edge of all four sides, fasten wood molding or plastic bumper material from a boating-supply store (or collect three or four old bicycle tires; cut in half, snip sidewalls every few inches and staple around ply). You can install the sides around a second sheet of ply (with an inch trimmed off one end and one side) laid on the ground if you want to be able to shovel out the sand easily. There is little point of fastening bottom to sides.
Be sure you use outdoor-glued plywood that is smooth and splinter free, "finished-one-side" for the upper surface of the bottom sheet and inner surface of the sides—where kids will scoot around and might get splinters. Before beginning construction it is best to seal both sides of your plywood with a clear, weatherproofing finish to bind in splinters and retard decay.
A Wood-Beam Sand Crib
I've built plenty of plywood boxes, however never to hold sand. The one time I did build soil bins above ground was to contain compost mixed with glass cullet made by crushing old bottles (this was in 1969—just before the first Earth Day when municipal recycling began to catch on). I used it to grow lovely, straight carrots, but the design would make a sturdy, quick, and easily disassembled/recycled sandbox.
The carrot crib was made of stacked 8"-square, 8'-long fence posts sawed from native Northern white cedar—which (along with redwood and red cedar in the West, Osage orange in the Midwest, and others) just naturally resists the terrors of bugs and rot. Cheaper is pressure-treated lumber used in ground-contact construction. However, the pressure-treatment contains copper and arsenic, two metallic poisons that I didn't want near the carrots and you surely won't want holding in your kid's sand pile.
I notched the ends log cabin-like with the chain saw and stacked the posts three high on a flat and level area of sod. Their weight held them in place, but they were warped enough to wobble, so for good measure, I drilled 3/8" holes down through the corner joints and dropped in 6" spikes as lock pins.
To get sand, I recruited an assortment of kids and made them sit quietly in the pickup truck bed while we drove to a natural gravel and sand bank. After the kids chose the best sand in the hill, we all started shoveling it into buckets and dumping it in the truck. We picked out roots and clumps of sod and rocks large enough to do damage in small hands. Back home after a stop at the swimming hole, we dumped the larger rocks into the dry well I'd sunk in the center of the pit, then shoveled in the sand. It took three loads—wet sand and a half-dozen wet, bouncy kids being heavy enough that a third-of-a-yard (9 cubic feet) made the truck's rear springs complain a little.
If you don't have a truck, but live near a natural sand deposit, you can haul it buckets at a time in the trunk of a car. You may be able to get road sand from your town's landfill or highway department. Or, you can order it hauled in a dump truck from any aggregate or traprock supplier to the building trades. Clean "sharp" sand will be stone and dirt free. Or as a last resort, in-town pool and outdoor furniture retailers sell white beach sand in bags for city kids who need sandboxes as much or more than country kids.
The neighborhood cats may try to adopt a sand pile as a giant kitty-litter box. Don't let it start. Besides being unaesthetic in the extreme, cat feces may contain human pathogens and parasites and you surely don't want the kids playing anywhere near it. Our dogs woofed cats out of the yard during the day and the kid's green-eyed, orange she-cat chased them away at night—and, once she'd joined the kids playing in the sand a couple of times, she seemed to prefer the loose soil of our garden to the sand pit. But, I kept a constant check on cat activity. On the way in from the garden every evening, I'd smooth the sand with the garden rake. If I'd ever seen signs of a digging or romping cat, I'd have raked and hosed the sand clean and put on a cover.
The best sand cover I know is one of those inexpensive blue, woven vinyl tarps you can get for a few dollars at any hardware store. Leave one over the sand anytime it's not in use, holding it in place with stones all around or wood planks on top. The kids will be able to remove it and (if you nag them long enough) replace it. If rain water pools on top, burn a few small holes through the middle with a small flame or soldering iron. (The heat will seal the edges so the hole margin won't ravel and enlarge with use.)