You would require a Feat in order to use both in the same round.
You would need Quicken Spell-Like Ability so that you could cast one spell-like ability as a free action, and then use the other as a standard action. You would still need to touch the target twice - once for each spell-like ability.
A spell-like ability is just like casting a spell. In this case, the spell-like abilities require a standard action to use. The touch attack would be considered a part of that standard action.
Contagion (Sp): Beginning at 2nd level, the touch of a cancer mage carries a contagion spell once per day per class level. The DC for the target's saving throw is 13 + the cancer mage's Wisdom modifier.
Poison (Sp): Once per day per class level beginning at 3rd level, the touch of a cancer mage carries a poison spell. The DC for the target's saving throw is 14 + the cancer mage's Wisdom modifier.
(Sp) = Spell-Like Abilities: Usually, a spell-like ability works just like the spell of that name. A few spell-like abilities are unique; these are explained in the text where they are described.
The "strength" of a Cancer Mage is not its spell-like abilities. The "strength" of the Cancer Mage is getting the benefits of a diseases, and not suffering the consequences of a disease, due to:
Disease Host (Ex): At 1st level, a cancer mage suffers no ill effects of diseases, except for purely cosmetic ones such as boils, pockmarks, watery eyes, blackened skin, hair loss, foul smell, and so on.
Notice I put quotation marks around the word strength. Cancer Mages are infamously known for cheese in the way of possibly extremely high strength scores. I do not know of any DM's, including myself, that don't either ban the Cancer Mage outright, or houserule limitations on the benefits of diseases, such as:
Festering Anger: Each day after the onset of this malady, the character takes 1d3 points of consitution damage, but she gains a cumulative +2 enhancement bonus to strength.