As bowlturner said, good luck! There are a number of challenges here.
Where possible, I'd like to avoid buying lots of different stains and mixing them by trial and error.
I'm afraid with this sort of thing generally it's not possible without some experimentation. Even if you were matching a fairly commonplace wood there's no guarantee a product of the right name will give the colour you want. Real-world example here: trying to match some vintage English oak it's clear a commercial English Oak stain is completely the wrong sort of colour (too red), but with a little experimentation it is discovered that an initial coat of Pine followed by two coats of Old Oak, the first wiped off after application, worked perfectly.
So, this kind of thing will usually require buying a few different stains and then trying various combos, along with your final finish; these are called "test boards" or "test strips". As you can see from the image below you must test with the final finish as there can be a significant deepening of tone after the clear finish goes on, and with oil-based varnishes also a slight yellowing, both of which obviously need to be factored in to the final colour.
Or to put it another way, if you got a dead-on colour match with stains alone it would no longer match after applying most finishes (exceptions would be some waterbased polys and a light application of lacquer).
There are additional challenges here, trying to match a softwood with hardwoods.
Softwood v. hardwood
Pine is a softwood, so has very characteristic light and dark banding which hardwoods don't have. The lighter parts (the earlywood or springwood) is soft and absorbent, while the darker wood (the latewood or winterwood) is much harder and non-absorbent.
What this means in practical terms is that the light wood gets much darker than the dark wood when a stain goes on, at worst giving an effect called grain reversal, where what was the darker grain ends up lighter.
Pine is a blotch-prone wood, and as such you need to treat the wood prior to stain going on to help achieve a smoother colouring, a process called sizing in the old days.
The usual recommended solution for blotching these days is to use a commercial "pre-stain conditioner", but diluted shellac or thinned varnish do the job as well or better for far less money. An additional advantages of using thinned varnish is that you can use the same product that you've already bought to use as your final finish, so no need to buy yet one more thing.
Much more useful information here on Popular Woodworking: Staining Pine - Make this inexpensive wood look like a million bucks.