Not too difficult, just might have to be okay with relocating at first until you can build up experience. To get into actual private companies' own maintenance departments is absolutely an experience-required thing, so often you have to start out at larger MROs and repair stations that handle the major inspection and overhaul stuff that a company like Coca-Cola just couldn't do in a reasonable time frame (since most have a shop with no more than 8-15 guys) which isn't a bad thing as this is a good experience-builder anyway and can get you fairly intimate with the different airframes. Put in a few years at something like that and generally if you're a good wrench and a decent, sociable human being, it's easy to either get offers from company flight departments or apply and get a job in one on your own initiative.
My first internship was with Duncan Aviation which is a massive corporate-targeted company with three different full-service maintenance locations and numerous satellite avionics shops across the country. I interned at their main service location in Nebraska and it was massive, like, 8 hangars all said and done, and they saw just about every modern business jet you can think of. Recently I've been working at a smaller MRO in Maine but I kind of got duped at my interview that they had a better corporate program than they truly did (their main focus was RJs), but I'm soon starting a job at a Dassault-owned repair facility, so I figure put in a few years there and see what opens up.
Truthfully, any sector of maintenance CAN have good pay; if there's one thing I've learned in the short amount of time I've actually been working, it's to know your skill level, be confident in it, and do not be afraid to negotiate what you believe you're worth.