What you need is called BCD (Binary Coded Decimal).
There is a certain support for it in '51 - have a look at the DAA instruction.

A short hint:

;each second do the following:
   mov  a,Seconds
   add  a,#1
   daa
   cjne a,#60h,SecondsDone
   mov  a,Minutes
   add  a,#1
   daa

;   etc. - by now you should've get the idea

   mov  a,#0         ;clear the seconds
SecondsDone:
   mov  Seconds,a
   mov  P1,a

---------------------------------
A completely different approach:

Of course, you can also count as now up to 60 binary and before sending it out to port, split it like:

   mov   a,SecondsInDecimal
   mov   b,#10
   div   ab     ;isn't it wonderful that we have div in '51?!
   swap  a      ;tens will go into upper 4 bits
   orl   a,b    ;ones will go into lower 4 bits
   mov   P1,a

Have fun!

JW