Putting a 48 tooth on there should be pretty straightforward, just move the front derailleur up to accommodate it, and you'll probably need to lengthen your chain, which may well mean replacing the chain if the current one is already reasonably worn. There will then be a few things that you will officially be exceeding Shimano recommendations on, but they shouldn't cause too much of a problem. First, your current FD will not have the correct curvature, making it slightly easier for the chain to overshift and fall off of the outside of the big ring, but this is still unlikely and I wouldn't worry about it (but , Shimano does make some MTB FDs designed for 48 tooth large rings if you want to have it perfect). Second, your RD will not have enough chain wrap capacity, but this just means that you need to avoid the small-small gear combinations. If you're not using the small chainring anyway, then this also won't be a problem (to fix it, you could change your middle and inner rings to 26 and 36 tooth versions, or get a whole new crankset that comes stock with 26,36,48 rings).
Using a road crankset (with at least a 50 tooth large ring), as mentioned above, would cause more problems because then you really would need to change your front derailleur for a road model, and this would not be compatible with your current front shifter, so you'd also need to change that. In addition, you'd have to make sure that the cranks of the road crankset will clear your chainstays, because the road cranksets tend to be quite a bit narrower. Overall, I wouldn't go down that route, and would instead keep the MTB components and get a 48 tooth big ring.