Carbide is the only way, unless you have access to EDM equipment. It has its limitations. Very brittle, and doesn’t handle interrupted cuts well. You'll need to be careful with rpm speed and pressure. Expensive.
It may be possible to spot-anneal where the hole will go. If it’s in the handle area, thats hould not an issue.
To amplify on what Blue Sky said.
I've been able to "spot-anneal" for drilling, as well. You can use a propane torch, but MAPP or an oxygen-acetylene rig would work better.
Torch tips come in different sizes, and you'll want one that is either as small as you can get, or a little smaller than the hole you intend to drill.
Wrap a wet rag around the beginning of the area you don't want to get hot. This will help preserve the heat treat work you've already done.
Get your hole location cherry red, if you can. Air cooling should get you an annealed area, but make sure it's sitting in a place with no moving air. You want the best chance at a slow cool.
If it's possible, submerge the heat-treated section in water. If not, leave the rag where it is while the steel cools.
Carbide and oil is still a good idea when you drill. Even WD-40 will help. It seems odd to add lubricant when you want cutting action between materials, but we have proof that it works.
Even annealed leaf springs are
TOUGH! I'm going to assume (knowing the perils of assuming), that your leaf springs are 5160 steel, or something with similar properties. If you don't have a drill press, make friends with somebody who does. A drill press generates a whopping lot more force on the bit than your shoulders will ever allow you to, unless you throw weighted barrels during competitions that are sponsored by MET-Rx.
