My understanding of the Guard Card process is that being on felony probation is more of an issue than having an old felony conviction.
Cannot hurt to try after the convictions have been dismissed under Penal Code 1203.4.
You should contact the Department of Consumer Affairs, which licenses security guards, to find out if your felony conviction will prevent you from getting a guard card. It doesn't automatically disqualify you, but they could use it to deny you a license.
Even if you get the dismissal, you will still have to report your conviction when applying for a guard card, and you can never legally possess a firearm.
A dismissal under Penal Code §1203.4 is sometimes called an expungement, but the term is misleading. The conviction is still a part of the court's public records, which will also show the case was dismissed. You still must disclose the conviction when applying to be a police officer or for certain other jobs, or if asked on an application for a state license -- including a guard card application -- or to run for public office. It will not remove any restrictions on your right to own a firearm. The conviction can still be considered a prior offense; for instance, your prior convictions for sales offenses could be used to add a three-year enhancement to similar offenses in the future.
If you try to leave the conviction off your application, that would be considered dishonesty, which would definitely get your application denied.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like this site, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.