I have Novak Spud Sights on mine. The rear sight is an M16 dual aperture style integrated into a picatinny rail. The Bushnell TRS-25 and perhaps others will co-witness. Of course you'll also need their taller front sight too. Nice set-up but pricey!

 

Williams makes a very nice rear peep and rail set with a taller front fiber optic post. I use them on my 10/22 with a TRS-25 when I don't have my scope on it.

 

That is the combination I have in mind. Does the taller front fiber optic post come in the #63330 FIRE SIGHT PEEP SET?

 

I assume the stock 10/22 iron sights will not work with a TRS-25?

 

The stock sights are so low, you can't use them with the included rail from Ruger mounted to the receiver.

I've never set it up, so I could be wrong, but I'd guess the sights will have to be quite high on a 10/22 to co-witness with anything. Maybe you should consider something see-through instead? I think there are aftermarket rails where the center is missing, allowing you to see the sights through the rail. Then some see-through rings to mount a red dot tube or something would let you use both, but not co-witnessed. Just a thought.

Or maybe sights similar to this: Ruger® Collector's Series 10/22® Carbine Rifle Features
and a red dot with a quick release mount?