Wow... nobody knows anything about Suzuki?
Well I have spent the day working my google fu on it and here is what I found. There are two camps those that say only to use oils designed for marine engines and those that say any oil of the proper grade/weight is acceptable.
In the Suzuki manual it says use a NMMA FC-W or API SG, SH, SJ, SL, SM approved oil.
Well looking up the API site it lists many of the SG, SH, etc as obsolete. Further it says the most current rating is SN and that it is backwards compatible so if it meets/exceeds SN then it also meets/exceeds SG, SH, SJ, SL, and SM. Almost all of the major brands... Penzoil, Mobil, Castrol, Valvoline etc... are SN certified and any of them in a 10W-40 are (according to the Suzuki owners manual) acceptable for use.