I can't offhand think of a drop-in (i.e. no work needed) replacement.
Read the above replies first.
For a minimum of coding effort, but a hardware mod, you could move to the DS3232 , but I haven't looked at the Dallas-Maxim site for ages - have a look for yourself. See if something new and shiny has popped up.
Get the Data Sheet and App Notes on the Philips PCF8563 , 73 etc RTCs.
There are some useful notes about crystal choice and trimming methods.
Whether or not it'll work with the DS1307 I don't know. That would be for you to try (and let us know).
Or, you could use a 'manual' method.
If, for example, you know it drifts consistently by -20 seconds per week , then read,subtract and write back.
A little bodgy but better than nothing and better than what you have.
Do you have large temperature variations? If so look at the suggested chips which have Xtals with temp compenstation. Those Dallas ones also have age compensation too.
Otherwise you are into MSF or GSM/GPS modules or similar and I doubt if you need something that complicated or expensive for your project.