I wasn't a fan of the 501s, but Levi has a discontinued 567s with a button fly that are hot.
Any suggestions for other button fly jeans?
As someone old enough to remember the true classic 501s, I can vouch that they haven't been the same since Levi's moved production offshore years ago. The basic pattern has changed, the denim is different, shrinks differently, and the fit is inconsistent according to the county of origin. So I sort of lost interest in buying new ones, although I have a lifetime collection of old ones.
My favorites today are Diesel and Lucky. Both have a variety of button-fly styles, some of which are quite bulge-worthy. Interestingly, some of the non-stretch (100% cotton) Lucky jeans I have show a nicer bulge than the stretch ones (1% or 2% spandex), but that could just be the way I hang. Both brands are actually sized a bit generously (true waist size is bigger than tag size), so you really need to try them on until you find the right size/style/fit. (i.e. don't order online at first, etc.) Some of the Lucky jeans are unisex, so again be careful of the sizing.
I took a quick look at my "weekend" (i.e. NSFW) jeans I've been wearing recently, and for Diesel found style names Bumix, Safado, Kutler, and Buster. (Some of these are old, even vintage, and may no longer be available.) The Lucky style names seem less precise, but I found Easy Rider, Hendrix, Slim Bootleg, and Lowrise Bootleg. Of course, I'm a somewhat corpulent old daddy, so what is flattering on my may be completely wrong for others.
I also rather like Nasty Pig, but they are more designed to be fetish wear than everyday clothes. So, you won't find them to try on in your average clothing store.