Pick your replacements. Consider some other variants: base64 Variant table from Wikipedia.
While base64 encoder/decoders are trivial, replacement subsitution can be done in a simple pre/post processing step of an existing base64 encode/decode functions (inside wrappers) -- no need to re-invent the wheel (entirely). Or, better yet, as Mr. Skeet points out, find an existing library with enough flexibility.
If you have no alternative suitable "funny" characters to choose from (perhaps all the other characters are invalid leaving only the 62 alphanumeric characters to choose from), you can always use an escape character for a very slight (~3/64?) increase in size. For instance, 0 (A) would be encoded as "AA", 62 (+) would be encoded as "AB" and 63 (/) would be encoded as "AC". This too could be done as a pre/post step if you don't want to write your own encoder/decoder from the ground-up. The disadvantage with this approach is that the ratio of output characters to input bytes is not fixed.