Golf Pride will probably be your best bet. They have cord grips and are all around good grips. 

Hi.....I was a loyal Titleist full cord grip fan, until I got tired of searching for them....so I tried the Golf Pride New Decade Multicompound Cord grips, and love them. They come in a variety of colors, and the newer whiteout ones look cool too. I'm stuck on the way the black and white ones look with my black Titleist bag with white lettering.....

I have found that New Decade multicompound grips work about the best for me. I got  good advice from a Pro, 19Hole, who just happens to be an Ambassador also and his advice was to get this style grip. It lasts quitee a while and is very easily cleaned. I used to golf more and changed grips every 4 months, but now I still change every 6 months. Probably just a  thing, but I do like new grips.

I should have mentioned that 19Hole is a Titleist player and the Ambassador status is from FootJoy. His advice is very point on.

I dont know about any with cords in it but I'm a huge fan of my Golf Pride VDR's. They have been great for me and have held up great.

I can't help with the cord situation, but I have been using Winn V17 Xi7 grips until this past fall, and now Winn Dri-Tac grips. I play a lot (several times a week), and the Dri-Tac grips still look and feel brand new. I use these grips primarily due to my latex allergy.

If you want something that will last I recommend Lamkin's.  I play 3GENs but they also offer a cord.  After a full year (50 rounds) the grips are still like new.  Also had Lamkins on my last set of irons that I played for 7 years and never once had to worry about replacing them.

NEW DECADE® MULTICOMPOUND WHITEOUT™

I like my Golf Pride New Decade's as well. If you aren't a fan of the multi compound the Golf Pride Tour Velvet BCT Cord grips are great too.