I got the support shard from spending around 4 hours on the agility bikes and the combat shard from 5 hours standing on the strength platform at the beach. I've yet to get a single shard from doing normal sorts of tasks.
I got my combat shard from killing a double agent on clue scroll. It is actually much easier to get combat related shards (combat, bossing, etc) than skilling. I think a Jmod confirmed this regarding the drop rate.
I was working on slayer tasks in attempt to get x2 shards, but it never worked out that way. Then while traveling through Gielinor, I got a combat shard for teleporting via magic casting spell.
AFK activities seem to give lower chance of shards, maybe 5 hours or more each. I got most of my shards pretty quick moving around, like doing clue scrolls, killing a double agent, daily Reaper. This is the fair mechanics, there are active, AFK and semi-AFK ways to play RS3. The more active we are, the better chance we get better rewards.
I got the Combat (Strength) one from The Beach's Body Building thing. Took less than an hour. But please remember that RNG is crap. Could be 15 mins. Could be 15 hours. This game really is a joke.
Got my combat shard from scattering ashes at the chapel in Fort Forinthy. I think it is per xp drop, and ashes/bones at the altar have lots of XP drops.