FLC OF A B737-100 OVERSHOT DSCNT ASSIGNED ALT. DUE TO THEIR HIGH DSCNT RATE; THE AUTOPLT DESIGN WAS NOT CAPABLE OF LEVELING THE ACFT. THE AUTOPLT WAS DISCONNECTED AND THE ACFT WAS MANUALLY RETURNED TO THE ASSIGNED ALT. ATC INTERVENED AND ADVISED THEM THAT THEY SHOWED AN ALT LOWER THAN THAT SHOWN BY THE ACFT ALTIMETERS.

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WITH ALL THE WX PROBS; ATC WAS VERY BUSY. WE DSNDED TO 17000 FT ENRTE TO TRINITY VOR. ABOUT 10-12 MI FROM TRINITY VOR; ATC TOLD US TO CROSS TRINITY AT 10000 FT; 250 KIAS. WE WENT IDLE PWR/SPD BRAKE. WE WERE MAXING OUT THE VVI NEEDLE; AND AT 11000 FT; I NOTICED THE AMBER 'ALT SELECT' HAD NOT GONE TO GREEN CAPTURE. I BEGAN TO BREAK DSCNT RATE TO 3000-4000 FT ON VVI. AT 10500 FT THE ALT SELECT STILL HAD NOT CAPTURED. AT 10000 FT I DECIDED TO DISENGAGE AUTOPLT; BREAK DSCNT WITH A HIGH G PULLUP. THE DSCNT CONTINUED TO AROUND 9725 FT BEFORE THE ALT BEGAN CLBING BACK TO 10000 FT. ATC CALLED TO VERIFY OUR ALT AND WE TOLD THEM WE WERE THEN AT 9800 FT GOING BACK TO 10000 FT. THE MAJOR PROB I NOTED HERE WAS THAT ATC GAVE US THE DSCNT CLRNC TO 10000 FT WAY TOO LATE. THEY WERE VERY BUSY AND LATE WITH THE CLRNC. WE TRIED TO COMPLY; BUT IT WAS EVIDENT THAT OUR OLD MODEL B737 AUTOPLT COULD NOT KEEP UP WITH THE RAPID DSCNT DEMANDED. ATC SHOULD HAVE STARTED DSCNT EARLIER; AND WE SHOULD HAVE ADVISED THEM THAT WE MIGHT NOT BE ABLE TO COMPLY.