Legal Question in Real Estate Law in California

If the lease is at an end or the lease is a month to month agreement then there is nothing illegal for the landlord in raising the rent.

Your Zip code suggests Pomona, and although I seldom practice down there, my references do not show that Pomona has rent control. Therefore, I'd think the landlord can, with proper advance notice, raise the rental upon birth of the tenants' child. Obviously the landlord cannot usually raise rent fixed by a lease during the term of the lease, and may need to give 30 to 60 days' notice to raise a month-to-month rental. Whether $300 a month is "fair" may depend upon what the basic rent already is, and how that relates to current market conditions. Keep in mind that property values and the rental market seem to be at the beginning of an upswing in many communities in California.

Mr. Whipple is basically correct. You must be at the end of a lease, or on a month-to-month tenancy, and they must give 30-days notice if you have been there under a year, and 60-days if you have been there over a year. If it is more than a certain percentage of the current rent, the notice period may be longer. There is a lot of good information for tenants about their basic rights here: http://www.dca.ca.gov/publications/landlordbook/catenant.pdf