I use a hypodermic needle with the end bent (you can do that by hitting a hard surface). Then use it as a hook to raise it enough so you are able to grab them with your tweezers
I agree with Curro. Take a large gauge syringe needle and bend it to a 90 degree angle by pressing it against your lab bench. Scoop underneath your coverslip and lift it up so that you can grab it with your tweezers.
If this still doesn't work try coating your coverslips in a separate container (with gentle rotation in a 50 mL conical or large beaker) and then transfer them into the plate in the hood.
Thanks for the responses - unfortunately the needle/tweezer trick won't work as the coverslips appear to be welded to the plastic! Will try the suggestions of coating prior to placing in culture dishes - thanks!
Take a 35 mm diameter dish and then take a diluted solution of Poly-L-Lysine of 5 or 10 mL and add it to the 35 mm dish containing your coverslips (make sure coverslips do not overlap each other during coating phase). I believe I got our Poly-L-Lysine from Abbott, but just follow the directions on covering the surface area of the 35 mm Petri dish to make your dilution and then aliquot it out into 5 or 10 mL aliquots (if you play with it you could probably get by with using less) which should cover the entire bottom of the dish and your coverslips. After application, wait 20 minutes and then in a hood remove Poly-L with suction in the corner of the dish and add back PBS while giving the dish a few swirls. Wait 10 minutes. Repeat PBS wash. Now you can use as many of the coverslips you want and the rest leave in the PBS solution but wrap it up with sealant wrap (whatever you might call it) to seal the dish and leave the dish in the hood. The coverslips should be fine for use for a week and you can mix different sizes of coverslips. If the coverslips are not sticky enough up exposure time to 30 minutes or increase the concentration of Poly-l-Lysine. If still having problems, fibronectin coverslips can be made using the same protocol. Used this for patch clamping and calcium imaging 1D and 2D along with immunocytochemistry. A trick when getting coverslips out of well with tweezers, leave a little bit of media or solution in the bottom and tilt the plate (36 wells) toward you and approach at 10 o'clock at a 60 degree angle. It is easier to come from the side a little bit. Hope this helps. Good luck.