Steaming them will soften them up for your dogs.
The quick-and-easy way to do that would be to microwave (as another user suggested), or just over a pot of water briefly until they're soft enough
cooking.stackexchange.com/users/4489/Ray
You could try microwaving the buns.
Microwaves tend to make things,
especially bread-like things, soggy and soft, which normally is not great, but in this case might be helpful.
Another option might be to put some warm water underneath them in the toaster oven.
I'm not sure how logistically feasible this is, but in theory it could help to soften up the bottoms of the buns.
cooking.stackexchange.com/users/3627/intuited
I did not try it myself, but if you have an apple-core remover, you can make a hole in the bun and put the sausage in through the hole.
If your sausage is too big, it could be a mess, maybe 'stab' several times then.
Good luck!
cooking.stackexchange.com/users/4580/Mien
As a work-around you could cut a V-shape in it to fit the hot dog in.
cooking.stackexchange.com/users/4726/Fabib
put your bun in microwave no more than 20 seconds , then remove from microwave and pierce one end with a sharpening steel pushing straight through bun .
insert hotdog gently , there u have it neat tidy and so easy .
cooking.stackexchange.com/users/18556/trevor
Take a sharp knife, and cut a vague circle or square into one end of the bun (no problem how it looks) -
depending on preference, it can be deeply angled, or pretty shallow.
Work the plug of bread out.
Levering your knife towards the middle of the bun should pop it out, if not try a few times on opposite sides.
Take a butter knife, and slide it into the bun.
Wrap your hand around one side of the bun, and push the flat side of the knife towards your hand.
Rotate, pushing the bread away from the center, with your hand braced on the outside of the bun
(note having your hand there helps keep the bread from splitting, it may not be necessary if the bread is soft, if you already cut deeply, or if you don't mind if it tears a bit).
You now have a hollow hot dog bun.
It's probably easiest to add whatever sauces you want on your hotdog first
(toppings might be a little trickier depending on how dry they are).
when you slide the hotdog in, it will displace the sauces, and spread them all the way down and back up the bun.
You can be pretty generous with sauces, they won't leak out since they are enclosed in the hollow bun.
Drier toppings you might have to try to tuck down the sides of the bun as you're sliding in the hotdog to fit - or just layer on top per bite afterwards.
This basic principle is how they make the 'puka' style hotdog in Hawaii (though I think they're called 'hula' style now).
You can use the leftover plug of bread to stop the open end, keeping the sauces in while it's horizontal on a plate or while you make multiple hotdogs.
A shallower cut plug is easier to fit back into the open end, a deeper one is easier to hollow out - and if you don't care about putting it back, you can even slice the very end off the bun horizontally to get access to the softer crumb for hollowing it.
If you don't replace the bread plug, you can eat the extra, use it for breadcrumbs, or simply discard.
cooking.stackexchange.com/users/47365/Megha
The splitting happens a lot less if the buns are fresh.
Try to use your hot dog buns the same day you buy them.
Additionally, check the dates on the package when you buy them.
cooking.stackexchange.com/users/54262/linda_j_p
I have some store-bought, pre-slit hot dog buns. They are a little brittle, and if I open the slit wide enough to take the hot dog, the bun splits in two.  I've tried using my toaster oven to warm the buns. They taste nice that way, but it they don't soften much.  Any other tricks?
How can I put a hot dog in a bun without splitting the bun?
cooking.stackexchange.com
<bread><hot-dog><convenience-foods>
cooking.stackexchange.com/questions/11958
cooking.stackexchange.com/users/2054/Jay Bazuzi
The quick and easy way would be to steam or microwave the buns quickly, and/or cut a hole or v-shape in the bun to fit the hot dog. You can use a microwave to soften them or cut a piece out of the bun to slide the hotdog in.
Try warming them in the microwave to soften them up. Use an apple corer or cut a shape into the bun to slide the hotdog in.