OK, dont go cheap. Im pretty sure the finish they use on those production guitars is the same or similar to the new automotive paints. Now, Ive been told you can have autobody supply places mix and place paint in rattle cans. I have never asked or gone that way but on a automotive forum I used to visit they were saying this can be done. HOWEVER, alot of that stuff uses hardeners, so Im not sure how that works with rattle cans, with a spray gun you mix it and have so long to use it and get you gun clean, when its activated its a done deal. You dont want to spray that stuff without a proper mask, it will kill you. Just look in your yellow pages and find autobody supply places and go see them with your dilema. DO NOT, let them talk you into enamel, its soft and takes for ever to harden and can NOT be buffed or rubbed out. I have to go now but I'll check in tomorrow night. Your best bet being as you dont have compressor or spray gun may very well be go and beg a autobody shop to spray it for you but I bet you wont like the price.
You can go to say Walmarts and get automotive paint in a spray can... get your color solid, many coats at proper intervals. let that dry overnight, then the following night sand that with 400 (no courser) or even 600... carefully as not to go through to wood again on the edges especially. But you still need to sand it completely till the shine is gone and its smooth as a babys butt. Then using the same kind/manufacturer of paint.... clearcoat it again following proper intervals. This will not be the really hard typical guitar finish or compare to the stuff I was talking about above but it should not get gummy. I have no idea what you must have used before, it prolly wasnt compatible between the clear and color paints you used or maybe you got some latex house paint or something... lol. You should also know they usually use primer/sealer before they put the color down... Im not sure what to tell you there, paint compatibility is everything, I suppose you could get that same type of primer at a chain store too, maybe get it all at a regular automotive parts store. Just get it all at the same place, same kind, compatible & manufacture of paint. I have no idea what they have for paints. Once again you'll need to let that dry over night and sand w/400 completely before you put you color coats. Use your eyes, if you dont have the glaze completely cut you wont get good adhesion. Those scratch pads work great for this too, get ultra fine. Use tack cloth after sandings to remove all dust, hang from a opened up coat hanger, or wire, then tack it off and spray evenly, use a lead light or bright flash light in one hand to see where you might be missing. Like if its hanging its common to not get good coverage at the top and bottom sides because you can't see them as well, then your done and get looking at it and... oops !
One coat in one direction the next in the opposite, (horizontal... vertical)keep it moving side to side or up down which ever the case that coat, and just dust it on there, dont get pushy, dont get real close, if it runs your screwed till it dries and then you start sanding again.... do not try to touch or wipe or brush a run out... been there done that, never worth it. Just let it dry, sand it out and try again.
Theres so many things, i could go nuts trying to explain. You might have problems with the automotive paints as many if not most are metallic, you might not like this, and to me this is kinda tacky on a guitar.... (black rules!) Theres those funny specialty finishes but they might not take well to sanding and clearcoat and not last if you dont clear coat them. Take you time choosing and read the cans for compatibility and options.
I dont know what to tell you, I have the stuff(tools) and can use high quality two part activated paints, like epoxys & urethanes. That dyed laquer Stewmac has is for transparent finish on fine figured woods and such and is not what you need for that basswood. Due to vapor regulations the stuff that comes in typical spray cans these days is not REAL hard. It should be good for a few years though and not get gummy... I still dont get that one.