It's okay to con wash every day, but your technique and the con you use are very important.
1. Don't use a purely moisturizing con if you intend to use it every day. You can balance it out with protein treatments as others have mentioned, but it's actually simpler to just use a more balanced conditioner to begin with. In general, that means avoid conditioners with heavy humectants like glycerin, and go easy on the cones. Soy, wheat, and rice proteins are good things (mild but helpful).
2. I know a lot of people "wash" with conditioner and then condition, but I get better results and less of that "overmoisturized" feeling if I simply rinse the hair throroughly and then condition.
3. When I follow the above 2 rules, I can shampoo and condition every 7-10 days and deep con with a fairly balanced conditioner without having to do anything too intensive on either the moisturizing or protein end.
BTW I'm not con washing presently because my current conditioner is very much a pure moisturizing con and not really suited for con washing. I always shampoo before using it.
But conditioners that work well for con washing that I've used include Jason Biotin, Jason Lavender, and Giovanni 50:50 Balanced Hair Remoisturizer.