90 Riviera startign problems

I have a 1990 Buick Riviera that I have owned for 1 year and love to drive. It has 130,000 miles on it and really has had no problems until recently. Sometimes (especially when it has been siting overnight or all day in the parking lot at work) it does not want to start. It turns over but doesn't "catch" right away, like it isn't getting fuel to the engine. Sometimes it may catch, cough and quit, it eventually does start. I have had it into the shop and he has run the diagnostics, but of course it doesn't do it when he hooks it up. He did mention he thought it was the "Coil Pack Assembly." The other thing that came up was the fuel pump, but it has never given me any problems once it is running. Any ideas?

Guess what...had 2 fuel pumps replaced and when it did it a third time it turned out to be a bad spark plug. problem fixed and has run grat for a year now.