Anybody have any good ideas about this? I ussually sling heavier rocks to build slinging muscle but this bothers my elbow like tennis elbow.
I don't really work out but I do exercice. I kayak twice a week and try to get about 25km in per trip (20 in the winter like now) but after that much paddling and a solid hour of slinging my elbow hurts. If I really over do it then it hurts a little the next day too. I also do pushups and crunches everyday and walk about 10km three times a week.

Is there any kind of weight training that helps?

Discus throw
Hammer throw
Put barbell on sholders, behind head.  Sit on bench.  Rotate back and forth as far and as quickly as posible about 35 times, back and forth.  Use 40LB total weight.
Tai Chi
Hiking with 75lbs of rocks in back pack, stopping to sling every so often.(remove pack to sling), stopping to select new rocks..INhale, L,R,L,R, exhale, L,R,L,R,inhale..
inhale thru nose, exhale thru mouth keeping tounge to roof of mouth.

I do karate and aikido, both good for self defense but karate is great for strengthening your arms. Since i started i've really noticed the difference. I also used to do kendo which was very tough on the arms, used to wake up the next day with them feeling like jelly.
I make circles with some heavy weights, arms out straight start off with small circles then move on to larger aswell as other excercises with weights. I think this would be most helpfull.

well i just take a brake. When my arm hurts from slinging i just take a brake for a day and the next day im fine. then when the pain becomes unbarable take a brake. What does not kill you can only make you stronger. except cancer.

Last year i got some elbow pain  with my long sling after rather few shoots, specially if i tried long distance/heavy ammo shooting. Now i sling with a short one to increase accuracy and i have no pain at all even throwing a lot more times full power and with heavy rocks too.

I also practice Aikido, which has great stretches for the wrist to strengthen them and make them more flexible, but I don't know about them helping the elbows.

However, when I played tennis in high school, our coach had us do some modified pushups to strengthen the muscles around the elbows so they wouldn't hurt.

You stand facing a wall almost your full arm's length away with your palms against the wall.  Then you do a standing pushup by leaning into the wall, except your elbows don't bend out to the side, they bend straight down so they end up at your sides.  These kind of pushups kept me from getting tennis elbow

I think it might also depend on your style of throwing.

The way I throw, a 1 3/4 rotation with one spin completely behind the back, you end up with a throwing motion similar to a baseball so the pain is in the shoulder.

Don't forget your back muscles! Most shoulder injuries that happen athletes in shoulder-intensive sports (such as slinging) can be traced and prevented by strengthening the muscles of the back that lend support to the shoulder complex.