Birchwood Casey makes two different levels of bluing solution. They have "Perma Blue" and "Super Blue". The "Super Blue" works much better than the "Perma Blue" but it's harder to find and costs a little more. I found it in a local gun shop. I've used it several times and generally have had good to excellent results. I recently used it on an old Spalding TPM and the end result was amazing.
Make sure the putter is very, very clean. After I remove the old finish I wash with soap and water. Then I clean it really well with Birchwood Casey Cleaner Degreaser or just plain old denatured alcohol.
The most important thing, I've found, for home bluing is to not leave a mirror finish on the putter before bluing. The bluing just runs off. It's like trying to pour it on glass. It has to be able to soak into the metal. I use a dremel and then polish and polish by hand until it gleams like a mirror. Then I go back over it lightly with lower grade of steel wool and just barely remove the mirror finish. It's still super smooth but has doesn't have the mirror finish any more. The metal can now absorb the bluing. I apply the bluing with a cotton ball and have another cotton ball ready soaked with cold water. After applying the bluing I immediately wipe it off with the water soaked cotton ball. I dry it with a super soft old tshirt or dry cotton ball. I repeat until I get the level of darkness I want. After the final coat rub very, very ,very lightly with super fine steel wool. Sometimes a dry cotton ball will work. It depends on the metal. It will usually shine up beautifully. After you get it all shined-up apply "Birchwood Casey Baricade Rust Protection" and let dry overnight. Better yet dry it with a hair dryer turned on high. After the "Barricade" dries apply several coats of a good quality car wax. I've had really good results using this process.
Keep in mind that it really all depends on the grade of steel or alloy used in the putter. Some putters just won't take over the counter bluing. The cool thing about the "Birchwood Casey Super Blue" is that it will blue nickel plated surfaces. Depending on the alloy used they can turn out really nice. I've had some that turn out looking kind of like a "black pearl" finish. Good Luck!